We provide gravitation practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on gravitation skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of gravitation Questions

Question No | Questions | Class |
---|---|---|

1 | Make a list of the uses of artificial satellites. | 11 |

2 | A geostationary satellite is orbiting the earth at a height ( 6 mathrm{R} ) above the surface of earth, where ( R ) is the radius of the earth. The time period of another satellite at a height of ( 2.5 mathrm{R} ) from the surface of earth in hour is В. ( 1.5 sqrt{2} h ) c. ( 6 sqrt{2} h ) D. ( 12 sqrt{2} h ) | 11 |

3 | An artificial satellite moving in a circular orbit around the earth has a total ( (K . E .+P . E .) ) is ( E_{0} . ) Its potential energy is A. ( -E_{0} ) в. ( 1.5 E_{0} ) c. ( 2 E_{0} ) D. ( E_{0} ) | 11 |

4 | A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is ( 11 k m s^{-1}, ) the escape velocity from the surface ofthe planet would be A. ( 110 k m s^{-1} ) B. ( 0.11 k m s^{-1} ) c. ( 1.1 k m mathrm{s}^{-1} ) D. ( 11 k m s^{-1} ) | 11 |

5 | Variation in the Acceleration Due to Gravity: Outside the earth ( : g=g_{0}left(frac{R_{e}}{x}right)^{2} ) | 11 |

6 | The direction of acceleration due to gravity depends: A. on the direction of motion of a body B. on the direction of motion of body’s acceleration c. on the direction of motion of body’s velocity D. none of these | 11 |

7 | Which of the following statements is true? A. The satellite ( A ) has a shorter period than the satellite ( B ) B. The satellite ( B ) has a shorter period than the satellite ( A ) C. The two satellites must have the same period D. The two satellites must have the same linear speed E. The two satellites must have the same period and the same linear speed | 11 |

8 | Acceleration due to gravity as a function of ( r ) is given by A ( cdot frac{4}{3} pi G r(A-B R) ) B . ( 4 pi G r(A-B R) ) c. ( frac{4}{3} pi G rleft(A-frac{3}{4} B Rright) ) D ( cdot frac{4}{3} pi G rleft(A-frac{4}{3} B Rright) ) | 11 |

9 | Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth. | 11 |

10 | A satellite of the earth is revolving in circular orbit with a uniform velocity ( V ) If the gravitational force suddenly disappears, the satellite will A. continue to move with the same velocity in the same orbitt B. move tangentially to the original orbit with velocity ( v ). c. fall down with increasing velocity. D. come to a stop somewhere in its original orbit. | 9 |

11 | A tunnel is dug along a diameter of the Earth. The force on a particle of mass ( boldsymbol{m} ) placed in the tunnel at a distance ( x ) from the centre is: A ( cdot frac{G M_{e} m}{R^{3}} x ) в. ( frac{G M_{e} m}{R^{2}} x ) c. ( frac{G M_{e} m}{R^{3} x} ) D. ( frac{G M_{e} m R^{3}}{x} ) | 11 |

12 | Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of g is greater at the poles than at the equator. | 11 |

13 | Four particles, each of mass ( mathrm{m}, ) are placed at the four corners of a square of side ‘a’. Force exerted by this system on another particle of mass ( mathrm{m} ) placed at the midpoint of a side of square is – A ( cdot frac{16 G m^{2}}{5 sqrt{5 a^{2}}} ) в. ( frac{16 G m^{2}}{5 sqrt{3 a^{2}}} ) c. ( frac{16 G m^{2}}{5 a} ) D. zero | 11 |

14 | Read the given statements and mark the correct option Statement 1: If an earth satellite is on a lower orbit, the speed of satellite increases Statement 2: The speed of satelite is a constant quantity for all orbits of earth A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1. B. both statements 1 and 2 are true but statement 2 is not correct explanation of statement c. statement 1 is true but statement 2 is false D. Both statements 1 and 2 are false | 11 |

15 | How orbital and escape velocities are related? A ( cdot v_{e}=2 v_{0} ) B ( cdot v_{e}=sqrt{3} v_{0} ) c. ( v_{e}=1.31 v_{0} ) D. ( v_{e}=1.41 v_{0} ) | 11 |

16 | A geo-stationary satellite is orbiting the earth at a height of 6 R above the surface of earth, R being the radius of earth. The time period of another satellite at a height of ( 2.5 mathrm{R} ) from the surface of earth is A. 10 hr B ( cdot(-6 / sqrt{2}) h r ) ( c cdot 6 h r ) D. ( 6 sqrt{2} h r ) | 11 |

17 | If the distance of Earth from the Sun were half the present value, how many days will make one year? | 11 |

18 | Calculate the force of gravitation between the earth and the sun, given that the mass of the earth ( =6 times 10^{24} k g ) and of the ( operatorname{Sun}=2 times 10^{30} k g . ) The average distance between the two is ( 1.5 times 10^{11} m ) | 11 |

19 | The acceleration due to gravity on the moon is one sixth that on the earth. ( A ) high jumper canjump ( 2 mathrm{m} ) on earth. What distance can he jump on the moon? ( A cdot 2 m ) B. ( 6 mathrm{m} ) ( c cdot 12 m ) D. 18 | 9 |

20 | Choose the correct statement among the following options. A. All bodies repel each other in this universe. B. Our earth does not behave like a magnet. C. Acceleration due to gravity is ( 8.9 mathrm{m} / mathrm{s}^{2} ) D. All bodies fall at the same acceleration in vacuum in state of free fall. | 11 |

21 | Two persons having mass ( 50 mathrm{kg} ) each, are standing 1 m apart from each other Calculate the force of gravitation and also calculate the force of gravity on each. (Take ( G=6.67 times 10^{-11} N m^{2} k g^{-2} ) mass of earth ( M=6 times 19^{24} k g ) Radius of earth ( boldsymbol{R}=mathbf{6 . 4} times mathbf{1 0}^{mathbf{6}} boldsymbol{m} ) )? | 11 |

22 | If ( A ) is the areal velocity of planet of mass ( M . ) its angular momentum is ( mathbf{A} cdot M ) B. ( 2 M A ) c. ( A^{2} M ) D. ( A M^{2} ) | 11 |

23 | ( mathbf{1} boldsymbol{g} boldsymbol{f}= ) A. ( 250 N ) B. 980 dynes c. 56 dynes D. All | 9 |

24 | Solve: Estimate the mass of the earth, given, radius of the earth ( =mathbf{6 . 4} times mathbf{1 0}^{mathbf{6}} mathbf{m} ) acceleration due to gravity ( =9.8 m / s^{2} ) and gravitational constant ( =6.67 times ) ( 10^{-11} S . I . ) units. | 11 |

25 | At a place, value of acceleration due to gravity ( g ) is reduced by ( 2 % ) of its value on the surface of the earth (Radius of earth ( =6400 mathrm{km} ). The place is:- A. ( 64 mathrm{km} ) below the surface of the earth B. ( 64 mathrm{km} ) above the surface of the earth ( mathrm{c} .32 mathrm{km} ) above the surface of the earth D. ( 32 mathrm{km} ) below the surface of the earth | 11 |

26 | Which of the following laws are conserved, if the areal acceleration is zero A. Law of conservation of angular velocity B. Law of conservation of angular momentum c. Law of conservation of angular acceleration D. Law of conservation of angular displacement | 11 |

27 | Keplers second law regarding constancy of aerial velocity of a planet is a consequence of the law of conservation of: A. Linear momentum B. Angular momentum c. energy D. none of the above | 11 |

28 | A research satellite of mass ( 200 mathrm{kg} ) circles the earth in an orbit of average radius ( frac{3 R}{2}, ) where ( R ) is the radius of the earth. Assuming the gravitational pull on a mass ( 1 mathrm{kg} ) on earth’s surface to be ( 10 mathrm{N}, ) the pull on this satellite will be: A . ( 860 mathrm{N} ) B. 889 N c. ( 827 mathrm{N} ) D. 798 N | 11 |

29 | The moon is observed from two diametrically opposite points ( A ) and ( B ) on earth. The angle ( theta ) subtended at the moon by the two directions of observation is ( 1^{0} 54^{prime} . ) Given the diameter of the earth to be about ( 1.276 times 10^{7} m ) compute the distance of the moon from the earth. | 11 |

30 | A large spherical planet of radius ( mathrm{R} ) made of a material of density d, has a spherical cavity of radius R/2,with centre of cavity a distance R/2 from the centre other planet. Find the gravitational force one small mass ( mathrm{m} ) at the centre of the cavity. A. 2 RGmd/3 B. RGmd/3 c. 2RGmd D. 4 RGmd/3 | 11 |

31 | Acceleration due to gravity as a function of ( r ) is given by : A ( cdot frac{4}{3} pi G r(A-B r) ) B . ( 4 pi G r(A-B r) ) c. ( frac{4}{3} pi G rleft(A-frac{3}{4} B rright) ) D ( cdot frac{4}{3} pi G rleft(A-frac{3}{2} B rright) ) | 11 |

32 | How far must a particle be on the line joining earth to sun, in order that the gravitational pull on it due to sun is counterbalanced by that due to earth. Given orbital radius of earth is ( 10^{8} mathrm{Km} ) and ( M_{S}=3.24 times 10^{5} M_{E} ) A ( cdot 6.4 times 10^{5} mathrm{Km} ) В. ( 1.75 times 10^{2} mathrm{Km} ) ( mathbf{c} cdot 1.75 times 10^{9} mathrm{Km} ) D. ( 6400 mathrm{Km} ) | 11 |

33 | A body is lying on the surface of earth.Suppose that the earth suddenly loses its power of attraction, then A. the weight of body will become zero B. the weight of body will become infinite c. the mass of the body will become zero D. the body will vanish in air | 11 |

34 | A spherical uparrow ole of radius ( mathbf{R} / mathbf{2} ) is excavated from ( mathbf{t} uparrow ) e asteroid of mass M as shown in fig. T Me gravitational acceleration at a point on t ( uparrow mathbf{e} ) surf ace of ( mathbf{t} uparrow mathbf{e} ) asteroid just above ( mathbf{t} uparrow ) excavation is : A. GM/R ( ^{2} ) B. ( mathrm{GM} / 2 mathrm{R}^{2} ) c. ( mathrm{GM} / 8 mathrm{R}^{2} ) D. ( 7 mathrm{gW} 8 mathrm{R}^{2} ) | 11 |

35 | If the distance between the earth and the Sun were half its present value, the number of days in a year would have been A . 64.5 в. 129 c. 182.5 D. 730 | 11 |

36 | The value of acceleration due to gravity is ( 980 mathrm{cm} s^{-2} ). What will be its value if the unit of length is kilometer and that of time is minute? | 11 |

37 | A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is ( 1.50 times 10^{8} k m ) away from the sun? | 11 |

38 | Assertion Kepler’s second law can be understood by conservation of angular momentum principle. Reason Kepler’s second law is related with areal velocity which can further be proved to be based on conservation of angular momentum as ( (boldsymbol{d A} / boldsymbol{d t})=left(boldsymbol{r}^{2} boldsymbol{omega}right) / 2 ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

39 | The time period of an earth satellite in circular orbit is independent of: A. the mass of the satellite B. radius of its orbit c. both the mass and radius of the orbit D. neither the mass of the satellite nor the radius of its orbit | 11 |

40 | Moon is revolving in a circular orbit with a uniform velocity ( V_{0} ). If the gravitational force suddenly disappears, the moon will A. continue to move in the same orbit B. move with a velocity ( V_{0} ) tangentially to the orbitt c. fall down freely D. ultimately comes to rest | 9 |

41 | At what altitude will the acceleration due to gravity be ( 25 % ) of that at the earth’s surface (given radius of earth is ( R) ? ) A. ( R / 4 ) в. ( R ) c. ( 3 R / 8 ) D. ( R / 2 ) | 11 |

42 | Gravitational force between two point masses ( mathrm{m} ) and ( mathrm{M} ) separated by a distance ( r ) is ( F . ) Now if a point mass ( 3 mathrm{m} ) is placed next to ( mathrm{m} ), what will be the (a) force on M due to ( m,(b) ) total force on M? A. ( F=4 F ) B. ( F=5 F ). ( mathbf{c} cdot F=6 F ) ( mathbf{D} cdot F=7 F ) | 11 |

43 | The escape velocity of an object on a planet whose radius is 4 times that of the earth and ( g ) value 9 times that on the earth, in ( mathrm{kms}^{-1} ) is A. 33.6 B. 67.2 c. 16.8 D. 25.2 | 11 |

44 | A stone drop from height ‘h’ reaches to Earth surface in 1 sec. If the same stone taken to Moon and drop freely then it will reaches from the surface of the Moon in the time(The ‘g’ of Moon is ( 1 / 6 ) times of Earth) A. ( sqrt{6} ) second B. 9 second c. ( sqrt{3} ) second D. 6 second | 11 |

45 | The earth’s radius is ( mathrm{R} ) and acceleration due to gravity at its surface is g. If a body of mass ( m ) is sent to a height ( h= ) ( boldsymbol{R} ) ( frac{i}{5} ) from the earth’s surface, the potential energy increases by A . mgh в. ( frac{4}{5} m g h ) c. ( frac{5}{6} ) mgh D. ( frac{6}{7} ) mgh | 11 |

46 | A bomb blasts on moon. Its sound will be heard on earth after A. 3.7 minutes B. 10 minutes c. 138 minutes D. sound will never be heard | 11 |

47 | The mass of the earth is ( 6 times 10^{24} mathrm{kg} ) and that of the moon is ( 7.4 times 10^{22} mathrm{kg} ) distance between the earth and the moon be ( 3.84 times 10^{5} mathrm{km}, ) calculate the force exerted by the earth moon. ( (G= ) ( left.6.7 times 10^{-11} N m^{2} k g^{-2}right) ) | 11 |

48 | Let ( ^{prime} boldsymbol{A}^{prime} ) be the area swept by the radial vector connecting the earth and the sun in April and May months. Then, find the area swept by the same radial vector connecting the earth and the sun in November and December months interms of ( boldsymbol{A} ) A. ( A ) в. ( 2 A ) c. ( frac{30 A}{31} ) D. ( frac{31 A}{30} ) | 11 |

49 | When a satellite going round the earth in a circular orbit of radius ( r ) and speed ( v, ) loses some of its potential energy, then : A. both ( r ) and ( v ) will increase B. both ( r ) and ( v ) will decrease c. ( r ) will decrease and ( v ) will increase D. ( r ) will increase and ( v ) will decrease | 11 |

50 | The escape velocity from the earth for a rocket is ( 11.2 mathrm{km} / mathrm{s} ) ignoring air resistance. The escape velocity of ( 10 mathrm{mg} ) grain of sand from the earth will be ( mathbf{A} cdot 0.112 mathrm{km} / mathrm{s} ) B. ( 11.2 mathrm{km} / mathrm{s} ) c. ( 1.12 mathrm{km} / mathrm{s} ) D. ( 0.0112 mathrm{kms}^{-1} ) | 11 |

51 | The gravitational field intensity at a point ( 10,000 mathrm{km} ) from the centre of the earth is ( 4.8 N k g^{-1} . ) The gravitational potential at the point is A ( .-4.8 times 10^{7} J k g^{-1} ) B . ( -2.4 times 10^{7} mathrm{Jkg}^{-1} ) C ( .4 .8 times 10^{6} mathrm{Jkg}^{-1} ) D. ( 3.6 times 10^{6} mathrm{Jkg}^{-1} ) | 11 |

52 | In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected? A. Weight is doubled B. Weight is quadrapled c. weight becomes 16 times D. Weight remains same | 11 |

53 | The escape velocity of a body from earth is about ( 11.2 mathrm{km} / mathrm{s} ). Assuming the mass and radius of the earth to be about 81 and 4 times the mass and radius of the moon, the escape velocity in ( mathrm{km} / mathrm{s} ) from the surface of the moon will be: A . 0.54 B. 2.48 ( c cdot 11 ) D. 49.5 | 11 |

54 | If masses of two point objects are tripled and distance between them is doubled,then gravitational force of attraction between them will A. Increase by 225% B. Decrease by 56% c. Increase by 125% D. Decrease by 144% | 11 |

55 | The Jupiter’s period of revolution around the Sun is 12 times that of the Earth. Assuming the planetary orbits to be circular, find the acceleration of Jupiter in the heliocentric reference frame. | 11 |

56 | The height at which the value of acceleration due to gravity becomes ( 50 % ) of that at the surface of the earth. (radius of the earth ( =mathbf{6 4 0 0 k m} ) ) is A . 2650 в. 2430 c. 2250 D. 2350 | 11 |

57 | A ball thrown up vertically returns to the thrower after 6 s. Find (a) The velocity with which it was thrown up, (b) The maximum height it reaches, and (c) Its position after 4 s. | 11 |

58 | Assuming the mass of Earth to be ten times the mass of Mars, its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth is ( 10 mathrm{m} / mathrm{s}^{2} ). Then the acceleration due to gravity on the surface of Mars is given by. A ( cdot 0.2 m / s^{2} ) B. ( 0.4 m / s^{2} ) c. ( 2 m / s^{2} ) D. ( 4 m / s^{2} ) E ( .5 mathrm{m} / mathrm{s}^{2} ) | 11 |

59 | Two planets have masses ( M_{1} ) and ( M_{2} ) and radii ( boldsymbol{R}_{1} ) and ( boldsymbol{R}_{2} ) respectively. Then the time periods of near surface satellite of the two planets will be equal if A. ( M_{1} R_{2}^{2}=M_{2} R_{1}^{2} ) B. ( M_{1} R_{2}^{3}=M_{2} R_{1}^{3} ) ( mathbf{c} cdot M_{1}^{2} R_{2}=M_{2}^{2} R_{1} ) D. ( M_{1} R_{1}^{3}=M_{2} R_{2}^{3} ) | 11 |

60 | Consider a planet in some system which has a mass double the mass of the earth and density equal to the average density of the earth. If an object weighs ( mathrm{W} ) on the earth, then its weight on the planet is: ( mathbf{A} cdot W ) в. ( 2 W ) c. ( frac{w}{2} ) D. ( 2^{1 / 3} W ) | 9 |

61 | When an object moves with a constant acceleration, under the influence of force of gravitation of the earth only, the object is said to have: A . free fall B. accelerated fall c. projectile motion D. constant velocity | 11 |

62 | Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to ( r^{5 / 2}, ) then the square of the time period will be proportional to. A ( cdot r^{3} ) в. ( r^{2} ) ( c cdot r^{2.5} ) D. ( r^{3.5} ) | 11 |

63 | Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a speed of revolution T. If the gravitational force of attraction between the planet and the star is proportional to ( boldsymbol{R}^{-5 / 2}, ) then A ( cdot T^{2} ) is proportional to ( R^{2} ) B . ( T^{2} ) is proportional to ( R^{7 / 2} ) c. ( T^{2} ) is proportional to ( R^{3 / 2} / 2 ) proportional D. ( T^{2} ) is proportional to ( R^{3.75} ) | 11 |

64 | Assertion On satellites we feel weightlessness. Moon is also a satellite of earth. But we do not feel weightlessness on moon. Reason Mass of moon is considerable. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

65 | Two spherical bodies of masses ( 2 M ) and ( M ) and of radii ( 3 R ) and ( R ) respectively are held at a distance ( 16 R ) from each other in free space. When they are released, the start approaching each other due to the gravitational force of attraction, then find (a) the ratio of their accelerations during their motion (b) their velocities at the time of impact. | 11 |

66 | Out of the following statements, the one which correctly describes a satellite orbiting about the earth is A. There is no force acting on the satellite B. The acceleration and velocity of the satellite are roughly in the same direction c. The satellite is always accelerating about the earth D. The satellite must fall, back to earth when its fuel is exhausted | 11 |

67 | The gravitational force of attraction between two masses depend on the distance between them is ( G= ) gravitaional constant ( =boldsymbol{k} times ) ( 10^{-11} N m^{2} k g^{-2} . ) what is the value of ( k ? ) | 11 |

68 | What is the magnitude of the gravitational force between the earth and a ( 1 k g ) object on its surface? (Mass of the earth is ( 6 times 10^{24} k g ) and radius of the earth is ( 6.4 times 10^{6} ) m.) | 11 |

69 | If the radius of the earth were to shrink by ( 1 % ) its mass remaining the same, the acceleration due to gravity on the earths surface would A. decrease by ( 2 % ) B. remain unchanged c. increase by ( 2 % ) D. will increase by ( 9.8 % ) | 11 |

70 | A double star system consists of two stars ( A ) and ( B ) which have time periods ( T_{A} ) and ( T_{B} . ) Radius ( R_{A} ) and ( R_{B} ) and ( operatorname{mass} M_{A} ) and ( M_{B}, ) choose the correct answer, A ( cdotleft(T_{A} / T_{B}right)^{2}=left(R_{A} / R_{B}right)^{3} ) B. If ( T_{A}>T_{B} ) then ( R_{A}>R_{B} ) ( mathbf{c} cdot T_{A}=T_{B} ) D. ( T_{A}>T_{B} ) then ( M_{A}>M_{B} ) | 11 |

71 | A body is weighed at the poles and at the equator. The weight: A. at the equator it will be more than at the poles B. at the poles it will be greater than at the equator C. at the poles it will be equal to the weight at the equator D. depends upon the object | 11 |

72 | What is the tension between her ears? A ( .2 .1 k N ) B. ( 2.6 k N ) c. ( 2.9 k N ) D. None | 11 |

73 | Mercury orbits the sun in about one- fifth of the earth year. If ( 1 A U ) is defined as the distance from the earth to the sum, what is the approximate distance between mercury and the sun? A ( cdot 1 / 25^{1 / 3} A U ) B . ( 1 / 9^{1 / 3} A U ) ( mathbf{c} cdot 1 / 5^{1 / 3} A U ) D. ( 1 / 3^{1 / 3} ) AU | 11 |

74 | 1 kgwt is equal to A .980000 dynes B. 9.80 dynes c. 98 dynes D. none of these | 9 |

75 | The value of G depends on A. the nature of the interacting bodies B. the size of the interacting bodies C. the mass of the interacting bodies D. none of these | 11 |

76 | Two planets are revolving around a star in circular orbits. If the ratio of radii of orbit is ( 1: 4, ) then ratio of their time period will be A . 1: 1 B. 1: 4 c. 1: 8 D. 1: 16 | 11 |

77 | A planet’s density is 3 times that of the Earth. But the acceleration due to gravity on its surface is exactly the same as on the Earth’s surface. The radius of the planet in terms of the Earth’s radius ( R ) is A ( .2 . R ) в. ( 3 R ) c. ( frac{R}{3} ) D. none of the above | 11 |

78 | The ratio of value of gravitational constant ( G ) between Earth and Moon system and Earth and Sun system is- ( A cdot>1 ) в. ( <1 ) c. 1 D. can't be calculated | 11 |

79 | What is the minimum energy required to launch a satellite of mass ( mathrm{m} ) from the surface of a planet of mass ( mathrm{M} ) and radius ( mathrm{R} ) in a circular orbit at an altitude of 2R. ( mathbf{A} cdot frac{5 G m M}{6 R} ) B. ( frac{G m M}{2 R} ) ( mathbf{c} cdot frac{G m M}{3 R} ) ( mathbf{D} cdot frac{5 G m M}{7 R} ) | 11 |

80 | In MKS, the gravitational unit of force is A. ( k g f ) в. ( g f ) ( c . N ) D. dyne | 9 |

81 | KEPLER’S LAWS A planet revolves around the sun in an elliptical orbit. If ( v_{p} ) and ( v_{a} ) are the velocities of the planet at the perigee and apogee respectively, then the eccentricity of elliptical orbit is given by A. ( frac{v_{p}}{v_{n}} ) в. ( frac{v_{a}-v_{p}}{v_{a}+v_{p}} ) c. ( frac{v_{p}+v_{a}}{v_{p}-v_{a}} ) D. ( frac{v_{p}-v_{a}}{v_{p}+v_{a}} ) | 11 |

82 | Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to (R = radius of each sphere ( ) ) ( A cdot R ) B . ( R^{3} ) ( c cdot R^{4} ) D. None of these | 11 |

83 | An object has a mass ( m ) kg on earth. What will be its mass on the moon? A. ( m ) kg в. ( 6 m ) кg c. ( frac{m}{6} ) kg D. zero | 9 |

84 | An object is taken to height ( 2 mathrm{R} ) above the surface of earth, the increase in potential energy is [R is radius of earth] ( ^{mathrm{A}} cdot frac{m g R}{2} ) в. ( frac{m g R}{3} ) c. ( frac{2 m g R}{3} ) D. 2 mgR | 11 |

85 | ( left[M^{-1} L^{3} T^{-2}right] ) are the dimensions of A. Acceleration due to gravity B. Gravitational constant c. Gravitational force D. Gravitational potential energy | 11 |

86 | A particle falling down freely under the influence of gravity covers a distance of ( 20 mathrm{m} ) in 4 secs. Find its acceleration A ( cdot 9.8 m / s^{2} ) B . ( 15 mathrm{m} / mathrm{s}^{2} ) ( mathrm{c} cdot 5 mathrm{m} / mathrm{s}^{2} ) D. ( 3 m / s^{2} ) | 11 |

87 | The mass of planet Jupiter is ( 1.9 times 10^{27} ) kg and that of the Sun is ( 1.99 times 10^{30} mathrm{kg} ) The mean distance of Jupiter from the Sun is ( 7.8 times 10^{11} ) m. Calculate the gravitational force which Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also calculate the speed of Jupiter. ( boldsymbol{G}= ) ( mathbf{6 . 6 7} times mathbf{1 0}^{-mathbf{1 1}} mathbf{N m}^{mathbf{2}} mathbf{k g}^{-mathbf{2}} ) ( mathbf{A} cdot=5 times 10^{23} mathrm{N} ) B. ( =4.15 times 10^{23} mathrm{N} ) ( mathbf{C} .=15 times 10^{23} mathbf{N} ) D. ( =1 times 10^{23} mathrm{N} ) | 11 |

88 | Describe kepler’s law of planetrary motion? | 11 |

89 | The time period of an earth’s satellite in circular orbit is independent of: A. the mass of the satellite B. radius of it’s orbit c. both the mass and radius of the orbit D. neither the mass of the satellite nor the radius of its orbit | 11 |

90 | As the distance of the planet from the sun increases, the period of revolution decreases. A. True B. False | 11 |

91 | The distances of Neptune and Saturn from the Sun are respectively ( 10^{13} ) and ( 10^{12} ) meters and their periodic times are respectively ( T_{n} ) and ( T_{S} ). If their orbits are assumed to be circular, the value of ( frac{T_{n}}{T_{S}} ) is : A. 100 в. ( 10 sqrt{10} ) c. ( frac{1}{10 sqrt{10}} ) D. 10 | 11 |

92 | A body of mass ‘m’ is raised from the surface of the earth to a height ‘nR’ (Rradius of earth). Magnitude of the change in the gravitational potential energy of the body is (g-acceleration due to gravity on the surface of earth) A ( cdotleft(frac{n}{n+1}right) m g R ) B ( cdotleft(frac{n-1}{n}right) m g R ) c. ( frac{m g R}{n} ) D. ( frac{m g R}{(n-1)} ) | 11 |

93 | A planet is revolving in an elliptical orbit around the sun. Its closest distance from the sun is ( r ) and the farthest distance is ( R ). If the velocity of the planet nearest to the sun be ( v ) and that farthest away from the sun be ( boldsymbol{V} ) then ( boldsymbol{v} / boldsymbol{V} ) is : A ( cdot frac{R^{2}}{r^{2}} ) B. ( frac{r^{2}}{R^{2}} ) ( mathbf{c} cdot frac{R}{r} ) D. ( frac{r}{R} ) | 11 |

94 | Two masses ( M_{1} ) and ( M_{2} ) at an infinite distance from each other and initially at rest, start interacting gravitationally. Find their velocity of approach when they are distances apart. | 11 |

95 | State whether true or false. The weight of a body on the surface of the moon is ( frac{1}{6} t h ) of that on the earth’s surface. It is because acceleration due to gravity on the surface of the moon is six times that on the surface of the earth. A. True B. False | 9 |

96 | A ball with a weight of 20 N is thrown vertically upward. What is the acceleration of the ball just as it reaches the top of its path? A. ( 10 m / s^{2} ) downward B. ( 10 mathrm{m} / mathrm{s}^{2} ) upward c. ( 20 m / s^{2} ) downward D. ( 20 m / s^{2} ) upward E. zero | 11 |

97 | A stone weight ( 100 mathrm{N} ) on the surface of the earth. The ratio of its weight at a height of half the radius of the earth to its weight at a depth of half the radius of the earth will be approximately A. 3.6 B. 2.2 ( c cdot 1.8 ) D. None of these | 11 |

98 | A particle of mass ( 10 g ) is kept on the surface of a uniform sphere of mass 100 ( k g ) and radius ( 10 c m . ) Find the work to be done against the gravitational force between them to take the particle far away from the sphere A ( cdot 13.34 times 10^{-10} mathrm{J} ) B . ( 13.33 times 10^{-10} J ) c. ( 6.67 times 10^{-9} mathrm{J} ) D. ( 6.67 times 10^{-10} J ) | 11 |

99 | Two particles of equal mass go around in a circle of radius ( r ) under the action of their mutual gravitational attraction. If the mass of each particle is ( m ), the speed of each particle is A ( cdot sqrt{frac{G m}{r}} ) в. ( sqrt{frac{G m}{2 r}} ) c. ( sqrt{frac{G m}{4 r}} ) D. ( sqrt{frac{2 G m}{r}} ) | 11 |

100 | Assertion The value of acceleration due to gravity does not depend upon the mass of the body. Reason Acceleration due to gravity is a constant quantity. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

101 | If a satellite is revolving very close to the surface of earth, then its orbital velocity does not depend upon A. mass of satellite B. mass of earth c. radius of earth D. orbital radius | 11 |

102 | The Sl unit of gravitational potential is ( A . J ) B. ( J k g^{-1} ) c. ( J k g ) D. ( J k g^{-2} ) | 11 |

103 | If ( v_{e} ) is the escape velocity for earth when a projectile is fired from the surface of earth. Then the escape velocity if the same projectile is fired from its centre is A ( cdot sqrt{frac{3}{2}} v_{e} ) в. ( frac{3}{2} v_{e} ) c. ( sqrt{frac{2}{3}} v_{e} ) D. ( frac{2}{3} v_{e} ) | 11 |

104 | The minimum and maximum distances of a planet revolving around sun are ( r ) and ( R ) If the minimum speed of planet on its trajectory is ( v_{0}, ) then its maximum speed will be: A ( cdot frac{v_{0} R}{r} ) B. ( frac{v_{0} r}{R} ) c. ( frac{v_{0} R^{2}}{r^{2}} ) D. ( frac{v_{0} r^{2}}{R^{2}} ) | 11 |

105 | Calculate the force of gravitation between two objects of masses ( 80 mathrm{kg} ) and ( 1200 mathrm{kg} ) kept at a distance of ( 10 mathrm{m} ) from each other.Given ( (G=mathbf{6 . 6 7} times ) ( left.10^{-11} N m^{2} / k g^{2}right) ) | 11 |

106 | Suppose the gravitational potential due to a small system is ( k / r^{2} ) at a distance from it. What will be the gravitational field ? Can you think of any such system? What happens if there were negative masses? | 11 |

107 | The figure shows a planet in elliptical orbit around the sun S. The kinetic energy of the planet will be maximum when the planet is at: ( A cdot P_{1} ) в. ( P_{2} ) ( c cdot P_{3} ) ( mathbf{D} cdot P_{4} ) | 11 |

108 | If the distance of earth from the sun reduces to one fourth of its present value then the length of the year will become A . ( 1 / 6 ) of present year B. 1/8 of present year c. ( 1 / 4 ) of present year D. ( 1 / 2 ) of present year | 11 |

109 | Show that period of a satellite revolving around the Earth depends upon mass of the Earth. | 11 |

110 | When the earth is far away from the sun, its travels slower. This is due to A. Potential energy is higher, hence it travels slower B. Inertia of the earth make it to go in straight line C. Kinetic energy is lower and hence it travels slower D. tend to get attracted by other planets and hence it becomes slower | 11 |

111 | How the gravitational constant will change if a brass plate is introduced between two bodies? A. No change B. Decreases c. Increases D. No sufficient data | 11 |

112 | Two artificial satellites of unequal masses are revolving in a circular orbit around the earth with a constant speed. Their time periods. A. will be different. B. will be same c. will depend on their masses D. will depend upon the place of their projection | 11 |

113 | If the radius of earth shrinks by ( 1.5 % ) mass remaining same ), then the value of gravitational acceleration changes by A. 2 % B . – 2 % c. 3 % D. -3 % | 11 |

114 | The average density of the earth in terms of ( g, ) Gand ( R ) is: A ( cdot frac{4 pi G R}{3 g} ) в. ( frac{3 g}{4 pi G R} ) c. ( frac{3 g}{4 pi G R^{2}} ) D. ( frac{4 pi G R^{2}}{3 g} ) | 11 |

115 | A boy can jump to a height ( h ) from ground on earth. What should be the radius of a sphere of density ( delta ) such that on jumping on it, he escapes out of the gravitational field of the sphere? A. ( sqrt{frac{4 pi G delta}{3 g h}} ) B. ( sqrt{frac{4 pi g h}{3 G delta}} ) c. ( sqrt{frac{3 g h}{4 pi G delta}} ) D. ( sqrt{frac{3 G delta}{4 pi g h}} ) | 11 |

116 | A body weighs ( 63 mathrm{N} ) on the surface of the earth. What is the gravitational force (in N) on it due to the earth at a height equal to half the radius of the earth? | 11 |

117 | Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth is ( g ) and that on the new planet is ( g^{prime} ), then what is the value of ( frac{boldsymbol{g}^{prime}}{boldsymbol{g}} ) | 11 |

118 | Value of ‘g’ on moon is of the value of ‘g’ on earth. Fill in the blank. A. One third B. One sixth c. one fourth D. one tenth | 9 |

119 | If ( T ) be the period of revolution of ( a ) planet revolving around sun in an orbit of mean radius ( R ), then identify the correct graph from the following. This question has multiple correct options ( A ) B. ( c ) D. None of these | 11 |

120 | A uniform sphere of mass ( mathrm{M} ) and radius ( mathrm{R} ) is surrounded by a concentric spherical shell of same mass but radius ( 2 mathrm{R} . ) A point mass ( mathrm{m} ) is kept at a distance ( x(>R) ) in the region bounded by spheres as shown in the figure. The net gravitational force on the particle is A ( cdot frac{operatorname{CMm}}{frac{pi^{2}}{n}} ) B. ( frac{G M m}{R^{3}} ) ( c cdot frac{G(M+m)}{x^{2}} ) D. zer | 11 |

121 | Which of the following are not correct? This question has multiple correct options A. The escape velocity for the Moon is ( 6 k m s^{-1} ) B. The escape velocity from the surface of Moon is ( v ). The orbital velocity for a satellite to orbit very close to the surface of Moon is ( v / 2 ) C. When an earth satellite is moved from one stable orbit to a further stable orbit, the gravitational potential energy increases D. The orbital velocity of a satellite revolving in a circular path close to the planet is independent of the density of the planet. | 11 |

122 | If the ratio of the masses of two plane what will be the ratio of their accelera | 11 |

123 | Assuming the earth to be a sphere of uniform density, how much could a body weigh at a height equal to radius of earth when it weighs ( 250 mathrm{N} ) on the surface of the earth. | 11 |

124 | The possible relationship between magnitudes of ” ( V_{1} ) ” and ” ( V_{2} ) ” is: A ( cdot V_{1}>V_{2} ) в. ( V_{1}<V_{2} ) ( c cdot V_{1}=V_{2} ) D. Both (A) and (C) | 11 |

125 | A rocket is launched to travel vertically upward with a constant velocity of 20 ( mathrm{m} / mathrm{s} . ) After travelling for 35 seconds, the rocket develops a snag and its fuel supply is cut off. The rocket then travels like a free body. The height achieved by it is: | 11 |

126 | A small mass and a thin uniformed rod each of mass ‘m’ are positioned along the same straight line as shown. find the forced of gravitational attraction exerted by the rod on the small mass. | 11 |

127 | f a body be projected vertically upward from the surface of the earth so as to reach a height ( n R ) above the surface; the increase in its potential energy is ( left(frac{n}{n+a}right) m g R, ) where ( a=? ) | 11 |

128 | The force acting on a mass of 1g due to the gravitational pull on the earth is called lgwt. One gwt equals: ( A cdot 1 N ) B. ( 9.8 mathrm{N} ) c. 980 dyne D. none of these | 9 |

129 | Mass of moon is ( 7.34 times 10^{22} k g ). If the acceleration due to gravity on the moon is ( 1.4 m s^{-2}, ) the radius of the moon is: ( left[G=6.667 times 10^{-11} N m^{2} k g^{-2}right] ) A ( cdot 0.56 times 10^{4} m ) В. ( 1.87 times 10^{6} mathrm{m} ) c. ( 1.92 times 10^{6} m ) D. ( 1.01 times 10^{8} mathrm{m} ) | 11 |

130 | If mass ( mathrm{M} ) is split into two parts, ( mathrm{m} ) and ( (M-m) ) which are then separated by a certain distance. What ratio of ( mathrm{m} / mathrm{M} ) maximizes the gravitational force between the two parts. A . ( 1 / 3 ) B. ( 1 / 2 ) c. ( 1 / 4 ) D. ( 1 / 5 ) | 11 |

131 | A small mass ( m ) is moved slowly from the surface of the earth to a height ( h ) above the surface. The work done (by an external agent) in doing this is This question has multiple correct options A. ( m g h, ) for all values of ( h ) B. ( m g h, ) for ( h<<R ) c. ( frac{1}{2} ) mgR, for ( h=R ) D. ( -frac{1}{2} ) mgR, for ( h= ) | 11 |

132 | If the time taken by the planet to move from position ( mathrm{P} ) to ( mathrm{X} ) and ( mathrm{Q} ) to ( mathrm{Y} ) is equal then the ratio of ( A_{1} ) to ( A_{2} ) is: A. Greater than one B. Less than one c. Equal to one D. Data insufficient | 11 |

133 | The acceleration due to gravity at a depth of ( 1600 k m ) inside the earth is ( mathbf{A} cdot 6.65 mathrm{ms}^{-2} ) B. ( 7.35 mathrm{ms}^{-2} ) c. ( 8.65 mathrm{ms}^{-2} ) D. ( 4.35 mathrm{ms}^{-2} ) | 11 |

134 | The ratio of acceleration due to gravity at a depth ( h ) below the surface of earth and at a height ( h ) above the surface for ( boldsymbol{h}<<boldsymbol{R} ) A. constants only when ( h<<R ) B. increases linearly with ( h ) C. increases parabolically with ( h ) D. decreases | 11 |

135 | If a body is sent with a velocity of ( mathrm{km} mathrm{sec}^{-1} ), it would leave the earth forever. A . 11.9 в. 11.6 c. 11.4 D. 11.2 | 11 |

136 | Two planets of radii ( r_{1} ) and ( r_{2} ) are made from the same material. The ratio of the acceleration due to gravity ( g_{1} / g_{2} ) at the surfaces of the two planets is: A ( cdot r_{1} / r_{2} ) в. ( r_{2} / r_{1} ) C ( cdotleft(r_{1} / r_{2}right)^{2} ) D. ( left(r_{2} / r_{1}right)^{2} ) | 11 |

137 | At the Earth, a block of mass ( m ) which rest on the frictionless table, let ( boldsymbol{F} ) be the force required to produce acceleration ( a ). Calculate the force at the Moon to produce same acceleration if ( g_{m o o n} ) is one sixth of ( g_{e a r t h} ) A ( cdot frac{F}{12} ) в. ( frac{F}{6} ) c. ( frac{F}{3} ) D. ( F ) E . ( 6 F ) | 9 |

138 | The universal law of gravitation must be applicable to A. The earth and the moon B. The planets around the sun c. Any pair of bodies. D. The earth and the apple. | 11 |

139 | Keplers second law regarding constancy of arial velocity of a planet is a consequence of the law of conservation of A. energy B. angular momentum c. linear momentum D. none of these | 11 |

140 | As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly ( 36,000 mathrm{km} ) from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth ( =6.0 times 10^{24} k g, ) radius ( =6400 ) ( mathbf{k m} ) | 11 |

141 | Linear momentum of the planet is This question has multiple correct options A. Different for different points of the orbitt B. Conserved c. Not conserved D. None of these | 11 |

142 | The ratio of the radii of the planets ( P_{1} ) and ( P_{2} ) is ( k_{1} . ) The corresponding ratio of the acceleration due to the gravity on them is ( k_{2} ). The ratio of the escape velocities from them will be A ( cdot k_{1} k_{2} ) в. ( sqrt{k_{1} k_{2}} ) ( mathbf{c} cdot sqrt{left(k_{1} / k_{2}right)} ) D. ( sqrt{left(k_{2} / k_{1}right)} ) | 11 |

143 | A particle is dropped under gravity from rest from a height ( hleft(g=9.8 m / s^{2}right) ) and it travels a distance ( frac{mathbf{9 h}}{mathbf{2 5}} ) in the last second the height ‘h’ is: ( mathbf{A} cdot 100 m ) B. ( 125 mathrm{m} ) ( mathbf{c} cdot 145 m ) D. ( 167.5 mathrm{m} ) | 11 |

144 | The value of gravitational acceleration ‘g’ at a height ‘h’ above the earth’s surface is ( frac{g}{4} ) then ( (R= ) radius of earth) ( mathbf{A} cdot h=R ) в. ( h=frac{R}{2} ) ( c cdot h=frac{R}{3} ) D. ( h=frac{R}{4} ) | 11 |

145 | Given that there is a relationship between the orbital radius of a planet and its period of revolution and that the periods of revolution of Mercury, Earth, Jupiter and Neptune are nearly 0.24,1 11.8 and 165 years. It follows that the period of revolution of A. Venus is less than 0.24 years B. Mars is less than 12 years. C. Uranus is more than 165 years D. Uranus is less than 165 years but more than 12 years. Of these the correct statement(s) is 1 are : A. A and C B. D only c. c only D. B and D | 11 |

146 | The force of attraction between the two bodies ( (A, B) ) depend upon: A. mass of ( A ) B. mass of ( B ) c. distance between them D. all of the above | 11 |

147 | A sphere of mass ( 40 mathrm{kg} ) is attracted by a second sphere of mass ( 15 mathrm{kg} ), when their centres are ( 20 mathrm{cm} ) apart, with a force of 0.1 milligram weight. Calculate the value of gravitational constant. ( mathbf{A} cdot=8.53 times 10^{-11} N m^{2} k g^{-2} ) B. ( =6.53 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{-2} ) ( mathbf{c} .=7.53 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{-2} ) D. ( =9 times 10^{-11} N m^{2} k g^{-2} ) | 11 |

148 | Are the equations of motion applicable to bodies projected vertically up with any velocity, say ( 8 k m s^{-1}, ) for determining the maximum height? And why? | 11 |

149 | In Sl unit gravitational unit of force is called A. ( G f ) в. ( K g f ) ( c . N ) D. All | 9 |

150 | Assertion An astronaut in an orbiting space station above the earth experience weightlessness. Reason An object moving around the earth under the influence of earth’s gravitational force is in a state of ‘free fall’. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

151 | An artificial satellite moving in circular orbit around the earth has a total kinetic + potential ) energy ( boldsymbol{E}_{0} ). Its potential energy and kinetic energy respectively are A ( cdot 2 E_{0} ) and ( -2 E_{0} ) B . ( 2 E_{0} ) and ( 3 E_{0} ) ( mathbf{c} cdot 2 E_{0} ) and ( -E_{0} ) D. ( -2 E_{0} ) and ( -E_{0} ) | 11 |

152 | Which of the following quantities remain constant in a planetary system when seen from the surface of the sun. This question has multiple correct options A . KE B. angular speed c. speed D. angular momentum E. binding energy | 11 |

153 | On the surface of the earth, force of gravitational attraction between two masses kept at distance dapart is 6 Newtons. If these two masses are taken to the surface of the moon and kept at the same distance d, the force between them will be A . ( 1 mathrm{N} ) B. 36N ( c cdot frac{1}{6} N ) D. 6N | 9 |

154 | On the pole of the Earth a body is imparted velocity ( v_{0} ) directed vertically up. Knowing the radius of the Earth and the free-fall acceleration on its surface, the height to which the body will ascend is given as ( h=frac{R v_{0}^{2}}{x g R-v_{0}^{2}} . ) The air drag is to be neglected. Find ( x ) | 11 |

155 | The possible relationship between magnitudes of ( ” boldsymbol{V}_{1} ) ” and ( ” boldsymbol{V}_{2} ) ” is : ( mathbf{A} cdot V_{1}>V_{2} ) ( mathbf{B} cdot V_{1}<V_{2} ) ( mathbf{c} cdot V_{1}=V_{2} ) D. Both A and C | 11 |

156 | Consider the following statements about acceleration due to gravity on earth and mark the correct statement(s): A. The value of ( g ) is constant throughout в. ( g^{prime}=gleft(1-frac{d}{r}right) ) ( mathrm{c} . g ) is slightly less (by about ( 1 % ) ) when distance ( <200 mathrm{m} ) D. ( g ) is slightly greater when distance ( <200 m ) | 11 |

157 | Which of the following quantities does not depends upon the orbital radius of the satellite? A ( cdot frac{T}{R} ) в. ( frac{T^{2}}{R} ) c. ( frac{T^{2}}{R^{2}} ) D. ( frac{T^{2}}{R^{3}} ) | 11 |

158 | Q Type your question- at a height ( boldsymbol{H} ) on the roof a building, tries to catch it. He misses the catch, the ball overshoots and simultaneously the person starts a stop-watch. The ball reaches its highest point and he manages to catch it upon its return. By this time, a time interval ( T ) has elapsed as recorded by the stop watch. If ( g ) is the acceleration due to gravity at this place, the speed with which the ball was thrown from point ( boldsymbol{A} ) will be ( mathbf{A} cdot sqrt{g H+g T} ) ( frac{(sqrt{g^{2} T^{2}+4 g H})}{2} ) ( frac{(sqrt{g^{2} T^{2}+8 g H})}{2} ) D. ( (sqrt{g^{2} T^{2}+2 g H}) ) | 11 |

159 | The gravitational force of attraction between two bodies at a certain distance is ( 10 mathrm{N} ). If the distance between them is doubled, the force of attraction: A. decreases by ( 50 % ) B. decreases by ( 75 % ) C. increases by ( 50 % ) D. increases by ( 75 % ) | 11 |

160 | Value of ( g ) on the surface of earth is ( 9.8 m / s^{2} . ) Value of ( g ) on the surface of earth is ( 9.8 m / s^{2} . ) At height ( h=R ) from the surface the value of ( g ) is ( frac{g}{x} . ) Find ( x ) | 11 |

161 | Let ( V ) and ( E ) denote the gravitational potential and gravitational field at a point. It is possible to have This question has multiple correct options A. ( V=0 ) and ( E=0 ) B. ( V=0 ) and ( E neq 0 ) c. ( V neq 0 ) and ( E=0 ) D. ( V neq 0 ) and ( E neq 0 ) | 11 |

162 | Given that mass of earth is ( M ) and its radius ( R ) body is dropped from a height equal to the radius of the earth above the surface of the earth. When it reaches the ground velocity of body will be ( ^{A} cdot frac{G M}{R} ) ( ^{text {В. }}left(frac{G M}{R}right)^{1 / 2} ) c. ( frac{2 G M}{R} ) ( ^{mathrm{D} cdot}left(frac{2 G M}{R}right)^{1 / 2} ) | 11 |

163 | The distance of planet Jupiter from the Sun is 5.2 times that of the earth. Find the period of revolution of Jupiter around the Sun. | 11 |

164 | Assertion The value of acceleration due to gravity does not depend upon the mass of the body. Reason Acceleration due to gravity is a constant quantity. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

165 | The moon’s radius is ( 1 / 4 ) times that of the earth and its mass ( 1 / 80 ) times that of the earth. If ( g ) represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is : ( mathbf{A} cdot g / 4 ) в. ( g / 5 ) c. ( g / 6 ) D. ( g / 8 ) | 9 |

166 | Four point masses each of mass ( mathrm{m} ) are kept at the vertices of a square. A point mass ( m ) is kept at the point of intersection of the diagonal of a square What will be the force experienced by central mass ( m ? ) | 11 |

167 | The value of G does not depend upon: A. nature of the interacting bodies B. size of the interacting bodies c. mass of the interacting bodies D. all of these | 11 |

168 | Four particles each of mass ‘m’ are placed at the four vertices of a square of side ‘a’. Find the net force on any one of the particle. | 11 |

169 | The depth at which the value of acceleration due to gravity becomes ( frac{1}{n} ) times the value at the surface is (R be the radius of the earth): A ( cdot frac{R}{n} ) в. ( frac{R}{n^{2}} ) c. ( frac{R(n-1)}{n} ) D. ( frac{R n}{(n-1)} ) | 11 |

170 | If the diameter of the earth becomes half of the present value but its average density remains unchanged then how would be the wieght of an object on earth been affected | 11 |

171 | If two stars of masses in the ratio 2: 3 become black holes, their radii will be in the ratio of: A .4: 9 B. 3: 2 c. 2: 3 D. 9: 4 | 11 |

172 | Cavendish Experiment to measure ( boldsymbol{G} ) uses the concept of A. Torque B. Force c. Force-Torque Equilirium D. None of these | 11 |

173 | The power of water pump is The power of water pump is ( 4 k W . ) If ( left(g=10 m s^{-2}right), ) the amount of water it can raise in 1 minute to a height of ( 20 m ) is: A. 100 litre B. 1000 litre c. 1200 litre D. 2400 litre | 11 |

174 | A tunnel is dug along a diameter of earth. The force on a particle of mass ( boldsymbol{m} ) and distance ( x ) from the centre in this tunnel will be : A ( cdot frac{G M_{e} m}{R^{3} x} ) в. ( frac{G M_{e} m R^{3}}{x} ) c. ( frac{G M_{e} m x}{R^{2}} ) D. ( frac{G M_{e} m x}{R^{3}} ) | 11 |

175 | A bomb blasts on the Moon. Its sound reaches the Earth A. after 10 minutes B. after 24 hours and 10 minutes c. after 3.7 minutes. D. cannot reach. | 11 |

176 | A ( 60 k g ) man is inside a lift which is moving up with an acceleration of ( 2.45 m s^{-2} . ) The apparent percentage change in his weight is: A . ( 20 % ) B. 25% c. ( 50 % ) D. ( 75 % ) | 11 |

177 | A body has a weight of ( 10 k g ) on the surface of the Earth. What will be its mass and weight when taken to the centre of the Earth? A. ( 10 mathrm{kg} ), zero B. zero, zero c. ( 10 mathrm{kg}, 10 mathrm{g} ) D. zero, ( 10 g ) | 11 |

178 | ( mathrm{R} ) is a radius of a planet and ( rho ) is its density. The escape velocity on its surface will be A ( cdot R^{2} sqrt{4 pi G rho / 3} ) в. ( R sqrt{4 pi G rho / 3} ) c. ( R^{2} sqrt{8 pi G rho / 3} ) D. ( R sqrt{8 pi G rho / 3} ) | 11 |

179 | If the escape velocity on earth is 11.2km / sec, its value for a planet having double the radius and 8 times the mass of earth is ( ldots . boldsymbol{m} / boldsymbol{s e c} ) A . ( 11.2 mathrm{km} / mathrm{sec} ) B. 22.4 km/sec c. ( 5.6 mathrm{km} / mathrm{seco} ) D. ( 8 mathrm{km} / mathrm{sec} ) | 11 |

180 | toppr Q Type your question quantities in relation to the energy of the comet-star system-kinetic energy (KE) gravitational potential energy ( (G P E), ) speed of comet (Speed), and mechanical energy of system (ME) Choose the table that is correctly filled in with ( x ) ‘s. Notice that in some boxes for certain | 11 |

181 | If the radius of the earth be increased by a factor of 5 by what factor its density be changed to keep the value of ( g ) the same? A ( cdot frac{1}{25} ) B. ( frac{1}{5} ) c. ( frac{1}{sqrt{5}} ) ( D ) | 11 |

182 | Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in ( mathrm{N} ) ) half way down to the center of the earth if it weighed 250 N on the surface? | 11 |

183 | From a solid sphere of mass ( M ) and radius ( R ) a spherical portion of radius ( boldsymbol{R} ) ( frac{1}{2} ) is removed, as shown in the figure. Taking gravitational potential ( V=0 ) at ( r=infty, ) the potential at the centre of the cavity thus formed is : ( (G= ) gravitational constant) ( ^{A} cdot frac{-2 G M}{3 R} ) в. ( frac{-2 G M}{R} ) ( c cdot frac{-G M}{2 R} ) D. ( frac{-G M}{R} ) | 11 |

184 | Weightlessness in a satellite is experienced because A . of inertia B. the gravitational force acting on the satellite is zero c. of centre of gravity D. centrifugal acceleration negates the acceleration due to gravity | 11 |

185 | Kepler’s second law states that the radius vector to a planet from the sun sweeps out equal areas in equal intervals of time.This law is a consequence of the conservation of A . Time B. Mass c. Angular momentum D. Linaer momentum | 11 |

186 | If the radius of the earth were to shrink by ( 1 % ), its mass remaining the same, the acceleration due to gravity on the earth’s surface would: A. Decrease by ( 1 % ) B. Remain unchanged C. Increase by ( 1 % ) D. Increase by 2% | 11 |

187 | The image shows an outline for which experiment? A. Cavendish Experiment B. Newton’s Experiment C. Kepler’s Experiment D. None of these | 11 |

188 | What is the effect of the shape of Earth on value of ‘ ( g ) ‘? | 11 |

189 | If a body is sent with a velocity of ( mathrm{km} mathrm{sec}^{-1} ), it would leave the earth forever. A . 11.9 в. 11.6 c. 11.4 D. 11.2 | 11 |

190 | The force primarily responsible for the existence of the solar system is the A. force of friction B. gravitational force c. electrostatic force D. magnetic force | 11 |

191 | A spring balance is calibrated at sea level. If this balance is used to measure the weight of a body at successive increasing heights from the surface of the earth, then the weight indicated by spring balance will A. decrease continuously B. increase continuously c. first decrease, then increase D. remains constant | 11 |

192 | Magnitude of binding energy of satellite is ( boldsymbol{E} ) and kinetic energy is ( boldsymbol{K} ). The ratio ( boldsymbol{E} / boldsymbol{K} ) is : A . ( 2 / 1 ) B . ( 1 / 4 ) ( c .1 ) D. ( 1 / 2 ) | 11 |

193 | If the earth has no rotational motion, the weight of a person on the equator is ( W ) Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight ( frac{3}{4} W . ) Radius of the earth is ( 6400 k m ) and ( g=10 m / s^{2} ) | 11 |

194 | The gravitational force of each planet in our solar system is different.The diagram below shows four planets listed in order from least amount of relative gravity to greatest amount of relative gravity. A person would weigh the most standing on which planet? Mercury Least Relative Gravity | 11 |

195 | Assertion The length of the day is slowly increasing. Reason The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

196 | The density of newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is It the radius of the plane would be A ( .2 . R ) в. ( 4 R ) c. ( frac{1}{4} R ) D・( frac{1}{2} R ) | 11 |

197 | The value of universal gravitational constant on earth for a particle of mass 5 kgs is В. ( 6.67 times 10^{-7} ) c. ( 5 times 6.67 times 10^{-11} ) D. ( 6.67 times 10^{-23} ) | 11 |

198 | If ( V_{e} ) is the escape velocity of a body from a planet of mass ( M ) and radius ( R ) Then, the velocity of satellite revolving at height ( h ) from the surface of planet will be A ( cdot V=V_{e} sqrt{frac{R}{(R+h)}} ) B ( cdot V=V_{e} sqrt{frac{2 R}{(R+h)}} ) ( ^{mathbf{c}} cdot_{V}=V_{e} sqrt{frac{(R+h)}{R}} ) D. ( V=V_{e} sqrt{frac{R}{2(R+h)}} ) | 11 |

199 | The height at which the weight of a body becomes ( frac{1}{16} t h, ) its weight on the surface of earth (radius ( boldsymbol{R} ) ), is ( A .3 R ) в. ( 4 R ) ( c .5 R ) D. ( 15 R ) | 11 |

200 | If ( g ) is the acceleration due to gravity at the Earths, surface, the gain of the potential energy of an object of mass ( mathrm{m} ) raised from the surface of the Earth to height equal to the radius ( mathrm{R} ) of the Earth is : A ( cdot frac{m g R}{4} ) в. ( frac{m g R}{2} ) ( mathrm{c} cdot m g R ) D. ( 2 m g R ) | 11 |

201 | Two fishes are ( 1 m ) apart underwater The gravitational force between them is ( F_{1}, ) Theyjump above the surface of water keeping the same distance (i.e 1 m) between them. The new gravitational force between them is ( F_{2} ). The relationship between ( boldsymbol{F}_{1} ) and ( boldsymbol{F}_{2} ) is A ( cdot F_{1}>F_{2} ) B. ( F_{1}<F_{2} ) c. ( F_{1}=F_{2} ) D. ( F_{1}: F_{2}=1: 2 ) | 11 |

202 | Two metal spheres of radius ( r ) are kept in contact. If ( ^{prime} d^{prime} ) is the density of each sphere material, the gravitational force between them is proportional to ( mathbf{A} cdot d^{2} r^{6} ) B. ( d^{2} r^{4} ) c. ( frac{d^{2}}{r^{4}} ) D. ( frac{r^{4}}{d^{2}} ) | 11 |

203 | Explorer ( 38, ) a radio-astronomy satellite of mass ( 200 k g ) circles the earth in an orbit of average radius ( frac{3 R}{2}, ) where ( R ) is the radius of the earth. Assuming the gravitational pull on the mass of ( 1 k g ) at the earth’s surface to be ( 10 N ), calculate the pull on the satellite. ( mathbf{A} cdot 889 N ) B. ( 8.89 N ) ( c .8889 N ) D. ( 88.9 N ) | 11 |

204 | The ratio of Sl unit of G to its CGS unit is A . 100: 1 в. 1000: 1 c. 10: 1 D. 10000: 1 | 11 |

205 | The force of gravitation between two bodies can be zero if the separation between the bodies becomes ( A ) B. ( c cdot-1 ) D. infinity | 11 |

206 | In the above diagram the shaded regions ( A ) and ( B ) are the areas covered by planet around the sun. ( boldsymbol{d}_{A} ) and ( boldsymbol{d}_{B}, boldsymbol{t}_{boldsymbol{A}} ) and ( t_{B} ) are the distances traveled by the planet and the time taken by it to cover the paths PQ and RS respectively. Choose the correct statement. ( mathbf{A} cdot d_{A}=d_{B} ) if ( t_{4}=t_{B} ) B ( cdot d_{4}t_{B} ) ( mathbf{c} cdot d_{A}=d_{B} ) if ( t_{A}d_{B} ) if ( t_{A}=t_{B} ) | 11 |

207 | A wooden plank of length 1 m and uniform cross section is hinged at one end to the bottom of a tank as shown in the figure. The tank is filled with water up to a height of 0.5 m. The specific gravity of the plank is ( 0.5 . ) If the angle ( theta ) by the inclination of that the plank makes with the vertical in the equilibrium position (exclude the case ( theta=0 ) ). Find the value of ( frac{1}{cos ^{2} theta} ) | 11 |

208 | A satellite is revolving around earth in a circular orbit. The radius of orbit is half of the radius of theorbit of moon. Satellite will complete one revolution in. | 11 |

209 | A particle is projected vertically upwards from the surface of teh earth (radius ( R_{e} ) ) with a kinetic energy equal to half of the minimum value needed for it to escape. The height to which it rises above the surface ot the earth is ( frac{boldsymbol{R}}{boldsymbol{n}} ) where ( n ) is: | 11 |

210 | A planet is revolving in an elliptical orbit around the Sun. Its closest distance from the Sun is ( r_{text {min }} ) and the farthest distance is ( r_{m a x} ). If the velocity of the planet at the distance of the closest approach is ( nu_{1} ) and that at the farthest distance from the Sun is ( nu_{2} ) ( operatorname{then}left{nu_{1}right} /left{nu_{2}right} ) A ( cdot frac{r_{max }}{r_{min }} ) B ( cdot frac{r_{min }}{r_{max }} ) C. ( frac{r_{min }+r_{max }}{r_{max }-r_{min }} ) D. none | 11 |

211 | A fisherman lifts a fish of mass ( 250 g ) from rest through a vertical height of 1.8 ( m ). The fish gains a speed of ( 1.1 m s^{-1} ) What is the energy gained by the fish? A. ( 0.15 J ) в. 4.3 .5 c. ( 4,4 J ) D. 4.6 .5 | 11 |

212 | Inside a horizontally moving box, an experimenter finds that when an object is placed on a smooth horizontal table and is released, it moves with an acceleration of ( 10 m s^{-2} . ) In this box, if 1 kg body is suspended with a light string, the tension in the string in equilibrium position. (w.r.t. experimenter) will be (take ( g=10 m s^{-2} ) A ( cdot 10 m s^{-2} ) B . ( 10 sqrt{2} mathrm{ms}^{-2} ) c. ( m s^{-2} ) D. Zero | 11 |

213 | Two equal point charges ( Q=sqrt{2} mu C ) are placed at each of the two opposite corners of a square and equal point – charges ( q ) at each of the other two corner.What must be the value of ( boldsymbol{q} ) so that the resultant force on ( Q ) is zero? | 11 |

214 | What is the percentage change in the value of ( g ) on shifting from equator to poles on the Earth’s surface? Difference in radius of Earth at poles and equator is ( 21 mathrm{km} ) A . 4.5% B . 0.65% c. 0.05% D. 0.43% | 11 |

215 | Estimate whether it takes more energy to get a satellite upto ( 1600 mathrm{km} ) above the earth than to put in orbit there earth’s radius is ( 6400 mathrm{km} ). Does your answer remain same for height ( 3200 mathrm{km} ) or for height ( 4800 mathrm{km} ? ) | 11 |

216 | ( frac{sqrt{4}}{frac{4}{4}} ) | 9 |

217 | A planet has mass and radius both half of earth. Acceleration due to gravity ( (g) ) at its surface should be A ( cdot 29.4 m / s^{2} ) в. ( 19.6 m / s^{2} ) C. ( 9.8 m / s^{2} ) D. ( 4.9 mathrm{m} / mathrm{s}^{2} ) | 11 |

218 | Give the dimensional formula for Gravitational constant ( G ) | 11 |

219 | The gravitational force between two stones of mass ( 1 k g ) each, separated by a distance of ( 1 mathrm{m} ) in vacuum is A . zero B . ( 6.675 times 10^{-5} N ) c. ( 6.675 times 10^{-8} N ) D. ( 6.675 times 10^{-11} N ) | 11 |

220 | The value of ( g ) at a height ( h ) above the surface of the earth is the same as at a depth ( d ) below the surface of the earth. When both ( d ) and ( h ) are much smaller than the radius of earth, then which one of the following is correct A ( cdot d=frac{h}{2} ) B. ( d=frac{3 h}{2} ) ( c ldots d=2 h ) ( mathbf{D} cdot d=h ) | 11 |

221 | If a planet consists of a satellite whose mass and radius were both half that of the earth, then the acceleration due to gravity at the surface of the planet would be A. ( 5.0 mathrm{ms}^{-2} ) B. ( 6.5 mathrm{ms}^{-2} ) c. ( 7.9 mathrm{ms}^{-2} ) D. ( 19.6 mathrm{ms}^{-2} ) | 11 |

222 | Two metal spheres each of radius ‘r’ are kept in contact with each other. If d is the density of the material of the sphere, then the gravitational force between those spheres is propositional to ( mathbf{A} cdot d^{2} r^{6} ) B. ( d^{2} r^{4} ) c. ( frac{d^{2}}{r^{4}} ) D. ( frac{r^{4}}{d^{2}} ) | 11 |

223 | Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is ( g ) and that on the surface of the new planet is ( g^{prime} ), then: A ( cdot g^{prime}=3 g ) B. ( g^{prime}=frac{g}{3} ) c. ( g^{prime}=9 g ) D. ( g^{prime}=27 g ) | 11 |

224 | The energy required to remove a body of mass ( m ) from earth’s surface is/are equal to: A. ( frac{-G M m}{R} ) в. ( m g R ) c. ( -m g R ) D. none of these | 11 |

225 | Which of the following hypotheses was made by Newton? A. Heavier body in the universe exerts a gravitational force on the lighter bodies. B. Every body in the universe exerts a gravitational force on every other body. c. Only the sun gravitational force is responsible for all the motion in this universe D. None of the above | 11 |

226 | Find the value of ( theta ) such that the acceleration of ( boldsymbol{A} ) is ( boldsymbol{g} / boldsymbol{6} ) downward along the incline plane. (All surfaces are smooth) A ( cdot theta=10^{circ} ) B . ( theta=60^{circ} ) ( mathbf{c} cdot theta=45^{circ} ) D. ( theta=53^{circ} ) | 11 |

227 | The period of a simple pendulum inside a satellite orbiting earth is A . zero B. ( infty ) c. can be any integer D. cant say | 11 |

228 | The mass of the jupiter is ( 1.9 times 10^{2} mathrm{kg} ) and that of sun is ( 1.99 times 10^{30} ) kg. The mean distance of jupiter from the sun is ( 7.8 times 10^{11} mathrm{m} . ) Speed of jupiter is (assuming that jupiter moves in circular orbit around the sun) | 11 |

229 | Choose the correct statements from the following This question has multiple correct options A. The gravitational forces between two particles are an action and reaction pair B. Gravitational constant ( (G) ) is scalar but acceleration due to gravity ( (g) ) is a vector C. The values of ( G ) and ( g ) are to be determined experimentally D. ( G ) and ( g ) are constant everywhere | 11 |

230 | Value of universal gravitational constant ( G ) in ( mathrm{CGS} ) unit is- A ( cdot 6.67 times 10^{8} mathrm{cm}^{3} g^{1} s ) B . ( 6.67 times 10^{8} mathrm{cm}^{3} g^{-1} s^{-2} ) c. ( 6.67 times 10^{9} mathrm{cm}^{3} g^{1} s^{2} ) D. ( 6.67 times 10^{7} mathrm{cm}^{3} g^{-1} s^{2} ) | 11 |

231 | State whether true or false. As a planet moves around the sun it sweeps equal areas in equal intervals of time. A. True B. False | 11 |

232 | Can a satellite move in a stable orbit in a plane not passing through the earth’s centre? Explain. | 11 |

233 | The change in the value of ( g ) at a height ( h ) above the surface of the earth is the same as at a depth d below the surface of the earth.When both ( h ) and ( d ) are much smaller than the radius of earth,then which one of the following is true? A ( . a=h / 2 ) В. ( d=3 h / 2 ) c. ( d=2 h ) ( mathbf{D} cdot h=d ) | 11 |

234 | In case of an orbiting satellite, if the radius of orbit is decreased A . its ( K E ) decreases B. its ( P E ) decreases c. its ( M E ) is doubled D. it stops moving in the orbit | 11 |

235 | A man of mass ( m ) starts falling towards a planet of mass ( M ) and radius R. As he reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass ( 2 M / 2 ) and a point mass ( M / 3 ) at the centre. Change in the force of gravity experienced by the man is A ( cdot frac{2 G M m}{3} frac{G M m}{R^{2}} ) B. 0 c. ( frac{1}{3} frac{G M m}{R^{2}} ) D. ( frac{4 G M m}{3} frac{G M m}{R^{2}} ) | 11 |

236 | Identify which of the following statement is correct for acceleration due to gravity on earth: A. It is abbreviated with the letter ( R ) B. It has a magnitude of ( 9.8 mathrm{cm} / mathrm{sec}^{2} ) away from the center of earth C. It has a magnitude of ( 9.8 mathrm{m} / mathrm{sec}^{2} ) toward the center of earth D. Acceleration tends to increase with a greater mass E. Acceleration tends to decrease with force | 11 |

237 | An object is weighed at the North pole by a beam balance and a spring balance, giving readings of ( W_{B} ) and ( W_{S} ) respectively. It is again weighed in the same manner at the equator, giving readings of ( W_{B}^{prime} ) and ( W_{S}^{prime} ) respectively. Assume that the acceleration due to gravity is the same everywhere and that the balances are quite sensitive. This question has multiple correct options A ( . W_{B}=W_{S} ) В. ( W_{B}^{prime}=W_{S}^{prime} ) ( mathbf{c} cdot W_{B}=W_{B}^{prime} ) D. ( W_{S}^{prime}=W_{S} ) | 11 |

238 | Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth is size. If the acceleration due to gravity on the surface of the earth is ( g ) and that on the new planet is ( g^{prime} ), then what is the value of g’lg? ( A cdot 3 ) B. 4 ( c cdot 5 ) D. 6 | 11 |

239 | Two planets ( A ) and ( B ) have their radii in the ratio of 2: 5 and densities in the ratio of 1: 6 respectively. Which of the following statements is NOT true regarding the given information? A. The ratio of acceleration due to gravity on them is 1 : 15 B. For the same volume of planets, mass of planet ( A ) is greater than that of planet ( B ) c. A body weighs 15 times more on planet ( B ) than on planet ( A ) D. Planet ( B ) has greater volume than planet ( A ) | 11 |

240 | A planet in its elliptical orbit has the farthest distance from the sun(r, ( ) ) equal to three times its nearest distance from the sun(r ( _{2} ) ). Will the orbital speed of the planet be different at those points? A. Orbital velocity at nearest point will be twice that at farthest point B. orbital velocity at nearest point will be thrice that at farthest point c. orbital velocity at farthest point will be thrice that at nearest point D. orbital velocity will be same, since no other force acts on the planet | 11 |

241 | Consider a satellite moving in a circular orbit around Earth. If ( mathrm{K} ) and ( mathrm{V} ) denote its kinetic energy and potential energy respectively, then(Choose the convention, where ( V=0 text { as } r rightarrow infty) ) A ( . K=V ) в. ( K=2 V ) ( mathbf{c} cdot V=2 K ) D. ( K=-2 V ) E . ( V=-2 K ) | 11 |

242 | At what height ( ^{prime} h^{prime} ) from the earth surface, acceleration due to gravity becomes half as that of acceleration due to gravity on the surface of earth. ( [R=text { Radius of earth }] ) ( mathbf{A} cdot h=R ) в. ( h=frac{R}{2} ) c. ( h=frac{R}{3} ) D. ( h=frac{R}{4} ) | 11 |

243 | A spring balance is graduated on sea level. If a body is weighted at consecutively increasing heights from earth’s surface, the weight indicated by the balance: A. Will go on increasing continuously B. Will go on decreasing continuously c. will remain same D. Will first increases and then decreases | 11 |

244 | Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object? | 11 |

245 | The speed of a falling body increases continuously. This is because: A. No force acts on it B. It is very light c. Air exerts a frictional force along the direction of motion D. The earth attracts it | 11 |

246 | Fill in the blanks: Value of gravitational constant (G) on moon is A. Greater B. Smaller c. same D. None | 9 |

247 | If density of the earth is doubled keeping its radius constant, then acceleration due to gravity (present value ( 9.8 m / s^{2} ) ) will be: A ( cdot 2.45 mathrm{m} / mathrm{s}^{2} ) B . ( 4.9 mathrm{m} / mathrm{s}^{2} ) c. ( 9.8 mathrm{m} / mathrm{s}^{2} ) D. ( 19.6 mathrm{m} / mathrm{s}^{2} ) | 11 |

248 | The value of ( G ) for two bodies in vacuum is ( 6.67 times 10^{-11} N / m^{2} / K g^{2} . ) Its value in a dense medium of density ( 10^{10} g m / c m^{3} ) will be: A ( .6 .67 times 10^{-11} N / m^{2} / K g ) B. ( 6.67 times 10^{-31} N / m^{2} / K g ) c. ( 6.67 times 10^{-21} N / m^{2} / K g ) D. ( 6.67 times 10^{-10} N / m^{2} / K g ) | 11 |

249 | Kepler’s law of area is based on A. Conservation of linear momentum B. Conservation of angular mementium c. conservation of energy D. both(1) and ( mid(2) ) | 11 |

250 | A body of mass ( mathrm{m} ) is dropped from a height h equal to the radius of the earth (R) above the tunnel dug through the earth as shown in the figure. Ignore the effect of earths rotation and air resistance, M is mass of earth. Choose the correct alternative(s): A. body will oscillate through the earth to a height hon both sides B. body will execute simple harmonic motion. c. Motion of the body is periodic. D. body passes the center of earth with a speed ( sqrt{frac{2 G M}{R}} ) | 11 |

251 | Suppose the earth shrinks such that its radius decreases to half the present value. What will be the acceleration due to gravity on the surface of the earth? | 11 |

252 | The Jupiter’s period of revolution around the Sun is 12 times that of the Earth. Assuming the planetary orbits to be circular, find how many times the distance between the Jupiter and the Sun exceeds that between the Earth and | 11 |

253 | For a satellite moving in an orbit around the earth, the ratio of K.E to P.E is: A ( -frac{1}{2} ) B. ( -frac{1}{sqrt{2}} ) ( c cdot 2 ) D. ( sqrt{2} ) | 11 |

254 | Which of the following is correct? A. The value of ( g ) is constant throughout B. ( g propto frac{1}{r^{2}} ) C ( . g ) is slightly less (by about ( 1 % ) ) when distance ( <200 m ) D. ( g ) is slightly greater when distance ( <200 m ) | 11 |

255 | The escape velocity for a planet is ( boldsymbol{v}_{e} cdot mathbf{A} ) tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be A ( cdot v_{c} ) в. ( frac{v_{e}}{sqrt{2}} ) c. ( frac{v_{e}}{2} ) D. zero | 11 |

256 | If ( F ) is the force between two bodies of masses ( m_{1} ) and ( m_{2} ) at certain separation, then the force between ( sqrt{2} m_{1} ) and ( sqrt{3} m_{2} ) at same separation is: A ( cdot sqrt{6} F ) в. ( sqrt{26} F ) ( c .6 F ) D. ( sqrt{216} F ) | 11 |

257 | Which of the following Kepler’s laws is also known as harmonic law? A. First law B. Second law c. Third law D. None of these | 11 |

258 | (a) Explain Newton’s first law of motion with an example. (b) ( F=frac{G m_{1} m_{2}}{d^{2}} ) is the mathematical form of Newton’s law of gravitation. Give the statement of Newton’s law of gravitation. | 11 |

259 | Four particles each of mass ( M, ) are located at the vertices of a square with side ( L . ) The gravitational potential due to this at the centre of the square is A ( cdot-sqrt{32} frac{G M}{L} ) в. ( -sqrt{64} frac{G M}{L^{2}} ) c. zero D. ( sqrt{32} frac{G M}{L} ) | 11 |

260 | Find the amount of work done by friction and gravity till the chain leaves the table, if the hanging part is pulled gently and released A ( cdot frac{5 m g ell}{18} ) в. ( frac{18 m g ell}{5} ) c. ( frac{m g ell}{5} ) D. ( frac{m g ell}{18} ) | 11 |

261 | Assertion Water kept in an open vessel will quickly evaporate on the surface of the moon. Reason The temperature at the surface of the moon is much higher than the boiling point of water A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

262 | Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will. A. Will become stationary B. Keep floating at the same distance between them c. Move towards each other D. Move away from each other | 11 |

263 | Assertion Smaller the orbit of the planet around the sun, shorter is the time it takes to complete one revolution. Reason According to Kepler’s third law of planetary motion, square of the time period is proportional to the cube of the mean distance from the sun. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

264 | A satellite is going around the earth. Which of the following statement is not correct? A. It is freely falling body B. It experiences no acceleration c. It is moving with constant speed D. Its angular momentum is constant | 11 |

265 | A satellite is revolving in a circular orbit at a distance of ( 2620 mathrm{km} ) from the surface of the earth. The time period of revolution of the satellite is (Radius of the earth ( =mathbf{6 3 8 0} ) km, mass of the earth ( =mathbf{6} times mathbf{1 0}^{mathbf{2 4}} mathbf{k g}, mathbf{G}=mathbf{6 . 6 7} times ) ( left.mathbf{1 0}^{-11} mathbf{N}-boldsymbol{m}^{mathbf{2}} / boldsymbol{k g}^{2}right) ) ( mathbf{A} cdot 2.35 ) hours B. 23.5 hours c. 3.25 hours D. 32.5 hours | 11 |

266 | The escape velocity for the earth is 11.2 ( mathrm{km} / mathrm{s} . ) The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is ( A cdot 280 mathrm{km} / mathrm{s} ) в. 56.0 km/s c. ( 112 mathrm{km} / mathrm{s} ) D. 24 km/s | 11 |

267 | The force of attraction between two unit point masses separated by a unit distance is called: A . gravitational potential B. acceleration due to gravity c. gravitational field D. universal gravitational constant | 11 |

268 | At what height from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be ( frac{g}{100} ? ) A. ( 10 R ) ( R ) в. ( 9 R ) c. ( 100 R ) D. ( R / 100 ) | 11 |

269 | The weight of a person on Earth is 600 N. His weight on Moon will appear as: A . zero B. 100 N c. 600 N D. 6300 N | 9 |

270 | At noon, the sun and the earth pull the objects on the earth’s surface in opposite directions. At midnight, the ( mathrm{gm} ) and the earth pull these objects in the same direction. Is the weight of an object, as measured by a string balance on the earth’s surface, more at midnight as compared to its weight at noon? | 11 |

271 | The separation between two masses is reduced to half. How is the magnitude of gravitational force between them affected? A. Force will become four times B. Force will remains same c. Force will become twice D. Force will become eight times | 11 |

272 | The work done in rearranging a system of 3 identical particles of mass 1kg on a right angled triangle to an equilateral triangle is (length of the side in both the configuration is ( 1 mathrm{m} ) ) A. ( W=G(1+1 sqrt{2}) ) в. ( W=G(1-1 sqrt{(} 2)) ) c. ( W=G(1-2 sqrt{(} 2)) ) D. ( W=G(1+2 sqrt{(} 2)) ) | 11 |

273 | The centripetal force acting on a satellite revolving round the earth is ( boldsymbol{F} ) The gravitational force on that planet is also ( F . ) The resultant force on the satellite is A . zero в. ( F ) c. ( 2 F ) D. ( frac{F}{2} ) | 11 |

274 | A planet is revolving in an elliptical orbit around the sun. Its closest distance from the sun is ( r ) and the farthest distance is ( R ). If the velocity of the planet nearest to the sun be ( v ) and that farthest away from the sun be ( V ) then ( boldsymbol{v} / boldsymbol{V} ) is : A ( cdot R^{2} / r^{2} ) B . ( r^{2} / R^{2} ) c. ( R / r ) D. ( r / R ) | 11 |

275 | A spherical planet far out in space has a ( operatorname{mass} M_{0} ) and diameter ( D_{0} . ) A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to: A ( cdot frac{G M_{0}}{D_{0}^{2}} ) в. ( frac{4 m G M_{0}}{D_{0}^{2}} ) c. ( frac{4 G M_{0}}{D_{0}^{2}} ) D. ( frac{G m M_{0}}{D_{0}^{2}} ) | 11 |

276 | The relation connecting acceleration due to gravity and gravitational constant is: A ( cdot g=frac{G M}{R^{2}} ) В . ( g=frac{G M}{R} ) c. ( g=G M R^{2} ) D. ( g=G M R ) | 11 |

277 | The ratio of the value of ( g ) in Sl units to CGS units is. ( mathbf{A} cdot 10^{2}: 1 ) B. 10: 1 ( c cdot 10^{-1}: 1 ) 1 D. ( 10^{-2}: 1 ) | 11 |

278 | WEIGHTLESSNESS An astronaut experiences weightlessness in a space satellite. It is because A. the gravitational force is small at that location in space B. the gravitational force is large at that location in space c. the astronaut experiences no gravity. D. the gravitational force is infinitely large at that location in space | 11 |

279 | Two satellites are revolving around the earth in circular orbits of same radii. Mass of one satellite is 100 times that of the other. Then their periods of revolution are in the ratio: A . 100: 1 B. 1: 100 c. 1: 1 D. 10: 1 | 11 |

280 | The inward force required to keep a satellite moving a circular orbit is? A. Gravitational field B. Centripetal force c. centrifugal force D. Aerodynamic forç | 11 |

281 | What would be the length of a sec. A pendulum at a planet (where acc, due to gravity is ( g / 4 ) ) if it’s length on earth is ( l ) A ( . l / 2 ) в. ( 2 l ) ( c cdot l / 4 ) D. 4 | 11 |

282 | If the mass of a planet is ( 10 % ) less than that of the earth and the radius is ( 20 % ) greater than that of the earth, the acceleration due to gravity on the planet will be. A. ( 5 / 8 ) times that on the surface of the earth B. ( 3 / 4 ) times that on the surface of the earth c. ( 1 / 2 ) times that on the surface of the earth D. ( 9 / 10 ) times that on the surface of the earth | 11 |

283 | In the region of only gravitational fields of mass ‘ ( M^{prime} ) a particle is shifted from ( boldsymbol{A} ) to ( B ) via three different paths of length ( 5 m, 10 m ) and ( 25 m . ) The work done in different paths is ( W_{1}, W_{2}, W_{3} ) respectively then: A. ( W_{1}=W_{2}=W_{3} ) В. ( W_{1}>W_{2}>W_{3} ) C ( . W_{1}=W_{2}>W_{3} ) D. ( W_{1}<W_{2}<W_{3} ) | 11 |

284 | Two blocks ( A ) and ( s ) of masses ( 100 k g ) and ( 20 k g ) respectively, separated by a distance of 5 in are kept on a smooth surface. A mass of 60kg is then added to the block ( A . ) Now, in order to experience same attractive force as before, the two blocks should be separated by a distance of : | 11 |

285 | The radius of the earth is ( R ) and acceleration due to gravity at its surface is ‘g’. If a body of mass ‘ ( m ) ‘ is sent to a height of ( boldsymbol{R} / mathbf{4} ) from the earth’s surface, the potential energy is: ( A cdot m g R / 3 ) в. ( m g R / 4 ) c. ( m g R / 5 ) D. ( m g R / 16 ) | 11 |

286 | A body weighs ( 900 mathrm{N} ) on the earth. Find its weight on a planet whose density is ( mathbf{1}^{s} ) ( frac{1}{3} ) the density of earth and radius is 1 ( t h ) ( frac{1}{4} ) that of the earth. A . ( 75 mathrm{N} ) в. 500 N c. 62 N D. 320N | 11 |

287 | On the earth surface, ‘g’ is a vector and its direction is oriented towards the centre of the ( A cdot ) body B. sun c. earth D. none of these | 11 |

288 | Explain why an astronaut in an orbiting satellite has a feeling of weightlessness. | 11 |

289 | If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that the earth, the gravitational acceleration on the surface of that planet is: A ( .0 .2 mathrm{g} ) в. 0.4 g ( c cdot 2 g ) D. 4 g | 11 |

290 | If the distance between Arun and Ajay becomes 10 times of initial value, then the gravitational force between them becomes ( _{-1-} ) times of the initial value. A. 100 B. 10 c. ( frac{1}{100} ) D. ( frac{1}{10} ) | 11 |

291 | Where is the intensity of the gravitational field of the earth maximum? A. Centre of earth B. Equator c. Poles D. Same everywhere | 11 |

292 | Write the three laws given by Kepler. | 11 |

293 | The earth’s gravitational force at some place in space causes an acceleration of ( 7 m / s^{2} ) in a ( 1 k g ) mass.What will be the acceleration of a ( 5 k g ) mass.What will be the acceleration of a ( 5 k g ) mass at the same place? A ( cdot 7 m / s^{2} ) B. ( 35 m / s^{2} ) c. ( 1.4 m / s^{2} ) D. ( 3.5 m / s^{2} ) | 11 |

294 | toppr Q Type your question B. ( c ) ( D ) | 11 |

295 | A hypothetical planet has density ( rho ) radius ( R, ) and surface gravitational acceleration g. If the radius of the planet were doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet’s surface would be? | 11 |

296 | What is the magnitude of the gravitational force between the earth and a ( 1 mathrm{kg} ) object on its surface? (Mass of the earth is ( 6 times 10^{24} ) kg and radius of the earth is ( left.6.4 times 10^{6}right) ) | 11 |

297 | A particle is projected upward from the surface of earth (radius ( =boldsymbol{R} ) ) with a speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise is A ( cdot sqrt{2} R ) в. ( frac{R}{sqrt{2}} ) ( c . R ) D. 2 ( R ) | 11 |

298 | The escape velocity from the earth is ( 11 k m s^{-1} . ) The escape velocity from a planet having twice the radius and same mean density as that of earth is ( mathbf{A} cdot 5.4 mathrm{kms}^{-1} ) B . ( 11 k m s^{-1} ) ( mathbf{c} cdot 22 k m s^{-1} ) D. None of the above | 11 |

299 | A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth ( left(m a s s=5.98 times 10^{24} k gright) ) have to be compressed to be a black hole? ( A cdot 10^{-9} m ) B. ( 10^{-6} mathrm{m} ) ( c cdot 10^{-2} m ) D. ( 100 m ) | 11 |

300 | Can you think of two particles which do not exert gravitational force on each other? | 11 |

301 | The motion of planets in the solar system is an example of the conservation of A . mass B. linear momentum c. angular momentum D. energy | 9 |

302 | A satellite is orbiting the earth at 17,500 MPH, a rock is released from the satellite. Identify what would happen to the rock. A. The rock would orbit the earth at a velocity of 17,500 MPH next to the satellite B. As the rock cannot generate its own force, it will slow down c. Gravity will pull the rock towards earth D. As the rock is smaller than the satellite, it will accelerate and orbit at a greater velocity E. As the rock is smaller than the satellite, its inertia will pull it further away from earth | 11 |

303 | The Jupiter’s period of revolution around the Sun is 12 times that of the Earth. Find the ratio gravitational force exerted on Earth to that on Jupiter | 11 |

304 | Find the distance between the centre of gravity and centre of mass of a twoparticle system attached to the ends of light rod. Each particle has the same mass. Length of the rod is ( R ), where ( R ) is the radius of the earth. ( A cdot R ) в. ( frac{R}{2} ) ( c . ) zer D. ( frac{R}{4} ) | 11 |

305 | If ( g ) on the surface of the Earth is 9.8 ( m s^{-2}, ) then it’s value at a depth of 3200 ( k m ) (Radius of the earth ( =6400 mathrm{km} ) ) is ( mathbf{A} cdot 9.8 m s^{-2} ) в. zero C ( .4 .9 mathrm{ms}^{-2} ) D. ( 2.45 mathrm{ms}^{-2} ) | 11 |

306 | The minimum and maximum speeds are ( ^{mathbf{A}} cdot sqrt{frac{G M}{9 R}}, sqrt{frac{2 G M}{R}} ) в. ( sqrt{frac{G M}{5 R}}, sqrt{frac{3 G M}{2 R}} ) c. ( sqrt{frac{G M}{6 R}}, sqrt{frac{2 G M}{3 R}} ) D. ( sqrt{frac{G M}{3 R}}, sqrt{frac{5 G M}{2 R}} ) | 11 |

307 | In case of a planet revolving around the sun, the net torque is A. zero B. Maximum c. Minimum D. Depends on the shape of the orbit | 11 |

308 | At a certain height above the earth surface the gravitational acceleration is ( 4 % ) of its value at the surface of the earth find the height above the earth surface: | 11 |

309 | If the mass of one particle is increased by ( 50 % ) and the mass of another particle is decreased by ( 50 % ), the gravitational force between them A. decreases by 25% B. decreases by 75 % c. increases by 25% D. does not change | 11 |

310 | When an object is in a bond state in a field, its total energy is A. positive B. negative c. zero D. infinite | 11 |

311 | A planet of mass ( M ) has uniform density in a spherical volume of radius ( R ) Calculate the work done by the external agent to de-assemble the planet in eight identical spherical part against gravitational pull amongst its constitute particle. | 11 |

312 | The moon’s radius is ( 1 / 4 ) that of the earth and its mass ( 1 / 80 ) times that of the earth. If ( g ) represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is: ( A cdot g / 4 ) B. ( g / 5 ) ( c cdot g / 6 ) D. g/8 | 11 |

313 | Dimensional formula of universal gravitational constant ( G ) is- A ( cdot M^{-1} L^{3} T^{-2} ) B . ( M^{-1} L^{2} T^{-2} ) c. ( M^{-2} L^{3} T^{-2} ) D. ( M^{-2} L^{2} T^{-2} ) | 11 |

314 | A spherical ball is dropped in a long column of viscous liquid. Which of the following graphs represent the variation of i) The gravitational force with time ii) The viscous force with time iii) The net force acting on the ball with time A. ( Q, R, P ) B. R, Q, P c. ( P, Q, R ) D. R, P, Q | 9 |

315 | Let a star be much brighter than our sun but its mass is same as that of sun If our earth has average life span of a man as 70 years, then on earth like planet of this star system at double the distance between our earth and sun will have an average life span of a man as A. 25 planet years B. 20 planet years c. 70 planet years D. 15 planet years | 11 |

316 | The velocity with which it must be projected is ( sqrt{frac{2 n g R}{n+1}}, ) where ( R ) is the radius of the earth and ( m ) the mass of body. | 11 |

317 | The weight of a satellite on earth is 100 kN. What is the gravitational force on the satellite when it orbits the earth at a distance of ( 12800 mathrm{km} ) from the center of the earth? A. 11 kilo-newtons B. 25 kilo-newtons c. 50 kilo-newtons D. 100 kilo-newtons E. 200 kilo-newtons | 11 |

318 | Planets A and B have same average density. Radius of ( A ) is twice that of ( B ) The ratio of acceleration due to gravity on the surface of ( A ) and ( B ) is A . 2: B. 1: ( c cdot 1: 4 ) D. 4: | 11 |

319 | Consider the satellites revolving round the earth at different heights.The ratio of their orbital speed is 3: 2 . If one of them is at a height of ( 200 mathrm{Km} ), the height of the other satellite is (Radius of the earth is ( R=6400 mathrm{Km} ) A. ( 8450 K m ) в. 845 Кт c. ( 84.5 K m ) D. ( 84500 K m ) | 11 |

320 | Three uniform sphere, each having mass ( m ) and radius ( r, ) are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is A ( cdot frac{G m^{2}}{r^{2}} ) в. ( frac{G m^{2}}{4 r^{2}} ) c. ( frac{sqrt{3} G m^{2}}{4 r^{2}} ) D. ( frac{sqrt{3} G m^{2}}{r^{2}} ) | 11 |

321 | If the distance between two particles is doubled,then the gravitational force becomes A . Half B. One fourth c. Double D. one eighth | 11 |

322 | The ratio of the gravitational force between the Earth and the satellite ( A ) to the gravitational force to the satellite ( boldsymbol{B} ) is equal to : A ( cdot frac{1}{4} ) B. ( frac{1}{2} ) c. 1 D. 2 ( E . ) | 11 |

323 | Four particles of masses ( m, m, 2 m ) and ( 2 m ) are placed at the four corners of a square of side ( a ) as shown in the figure. The magnitude of the gravitational force acting on a particle of mass ( boldsymbol{m} ) placed at the centre of the square is ( ^{mathbf{A}} cdot frac{2 G m^{2}}{a^{2}} ) в. ( frac{G m^{2}}{sqrt{2} a^{2}} ) c. ( frac{G m^{2}}{2 a^{2}} ) ( D ) | 11 |

324 | Planet moves in an elliptical orbit around one of the foci. The ratio of maximum velocity ( V_{max } ) and minimum velocity ( V_{min } ) ansd eccentricity e of the ellipse is given by A ( cdot frac{1-e}{1+e e} ) В ( cdot frac{e-e}{e+e e} ) c. ( frac{1+e}{1-e-e} ) D. ( frac{e}{e-e} ) | 11 |

325 | Three planets of same density have radii ( boldsymbol{R}_{1}, boldsymbol{R}_{2} ) and ( boldsymbol{R}_{3} ) such that ( boldsymbol{R}_{1}= ) ( 2 R_{2}=3 R_{3} ) The gravitational field at their respective surfaces are ( g_{1}, g_{2} ) and ( g_{3} ) and escape velocities from their surfaces are ( boldsymbol{v}_{1}, boldsymbol{v}_{2} ) and ( boldsymbol{v}_{3} ) then This question has multiple correct options A. ( g_{1} / g_{2}=2 ) В ( cdot g_{1} / g_{3}=3 ) c. ( v_{1} / v_{2}=1 / 4 ) D. ( v_{1} / v_{3}=3 ) | 11 |

326 | Suppose the distance between earth and sun becomes half of its present distance. What is likely to happen to life? | 11 |

327 | The escape velocity for a planet is ( boldsymbol{v} . mathbf{A} ) particle starts from rest at large distance from the planet The planet only under gravitational attraction and passes through a smooth tunnel through its centre, speed at the centre of the planet will be: | 11 |

328 | The acceleration due to gravity with an increase in height and depth. | 11 |

329 | How are ( g ) and ( G ) related? A ( cdot g=frac{G M}{R^{3}} ) в. ( g=frac{M}{G R^{2}} ) c. ( _{g}=frac{G M}{R^{2}} ) D. ( g=frac{G M}{R} ) | 11 |

330 | If a planet were suddenly stopped in its orbit supposed to be circular, show that it would fall into the sun in a time ( boldsymbol{T} times ) ( left(frac{sqrt{2}}{8}right), ) where ( T ) is the time period of revolution. | 11 |

331 | The change in the gravitational potential energy when a body of mass ( mathrm{m} ) is raised to a height ( n R ) above the surface of the Earth is (Here R is the radius of the earth) A ( cdotleft(frac{n}{n+1}right) ) mgR в. ( left(frac{n}{n-1}right) ) тg ( R ) c. ( n m g R ) D. ( frac{m g R}{n} ) | 11 |

332 | A meteor of mass ( M ) breaks up into two parts. The mass of one part is ( m ). For a given separation ( r ) the mutual gravitational force between the two parts will be maximum if A. ( m=(M / 2) ) в. ( m=(M / 3) ) c. ( _{m}=frac{M}{sqrt{2}} ) D. ( _{m}=frac{M}{2 sqrt{2}} ) | 11 |

333 | The semi-major axes of the orbits of Mercury and Mars in the astronomical units are 0.387 and 1.524 respectively. If the time period of Mercury is 0.241 year, then the time period of mars will be A. 0.9 Year B. 0.19 Year c. 1.9 Year D. 2.9 Years | 11 |

334 | A planet of mass ( M=2.4 times 10^{14} k g ) is orbiting a star in time ( boldsymbol{T}=boldsymbol{3} times mathbf{1 0}^{4} boldsymbol{s} ) sweeps an area of ( boldsymbol{A}=mathbf{6 . 9} times mathbf{1 0}^{mathbf{8}} boldsymbol{m}^{mathbf{2}} ) Calculate Angular Momentum of Planet | 11 |

335 | Which among these is required in the experiment to measure Gravitational Constant? This question has multiple correct options A. 2 big spheres B. 2 small spheres c. a rod D. physical balance | 11 |

336 | A satellite of mass m goes around the earth along a circular path of radius ( r ) (from the center of Earth), let me is the mass of the earth and ( R ), its radius. Then the linear speed of the satellite depends on: ( mathbf{A} cdot m_{e} ) and ( r ) B . ( m_{e} ) only ( mathbf{c} cdot mu, m_{e}, V ) D. ( m_{e}, R_{e} ) and ( r ) | 11 |

337 | Acceleration due to gravity on the moon is ( 1 / 6 t h ) of the acceleration due to gravity on the earth. If the ratio of densities of the earth and the moon is ( 5 / 3, ) then radius on the moon in terms of radius of earth will be | 9 |

338 | Which of the following statement is true? ( mathbf{A} cdot g ) is same at all places on the surface of earth. B. g has its maximum value at the equator. C. ( g ) is less at the earth’s surface than at a height above it or a depth below it. D. ( g ) is greater at the poles than at the equator. | 11 |

339 | If the acceleration due to gravity inside the earth is to be kept constant, then the relation between the density ( d ) and the distance ( r ) from the centre of earth will be ( mathbf{A} cdot d propto r ) B. ( d propto r^{1 / 2} ) c. ( d propto 1 / r ) D. ( d propto frac{1}{r^{2}} ) | 11 |

340 | Two satellites of the same mass are launched in the same orbit around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is A. ( -frac{2 G M m}{r} ) в. ( -frac{G M m}{r} ) c. ( frac{G M m}{2 r} ) D. ( frac{G M m}{4 r} ) | 11 |

341 | An asteroid is moving directly towards the centre of the earth. When at a distance of ( 10 R(R ) is the radius of the earth) from the earth centre, it has a speed of ( 12 k m / s . ) Neglecting the effect of the earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is ( 11.2 k m / s ) )? Give your answer to the nearest integer in kilometer/s | 11 |

342 | If the distance between the centres of earth and moon is ( mathrm{D} ) and mass of earth is 81 times that of moon. At what distance from the centre of earth gravitational field will be zero: A ( cdot frac{D}{2} ) в. ( frac{3 D}{2} ) c. ( frac{4 D}{5} ) D. ( frac{D}{10} ) | 11 |

343 | The largest and the shortest distance of the earth from sun are a and b, respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on the major axis meets the orbit is A ( cdot frac{a b}{a+b} ) в. ( frac{a b}{2(a+b)} ) c. ( frac{2 a b}{a+b} ) D. ( frac{a+b}{2 a b} ) | 11 |

344 | A body weighs ( 160 N ) on the earth. Find its weight on another planet whose mass is ( frac{5}{2} ) times mass of earth and radius ( frac{4}{5} ) times that of earth. A . ( 125 N ) B. ( 625 N ) c. ( 225 N ) D. 25 N | 11 |

345 | Identify the incorrect statement about a planet revolving around Sun A. The gravitational attraction provides the centripetal force for a revolving planet B. The total energy of a planet is always negative c. The total energy of a planet is always more than potential energy of the system D. Kinetic energy of revolving planet is sometimes zero | 11 |

346 | The average value of acceleration due to gravity on the surface of the earth is equal to: A. ( 9.8 mathrm{ms}^{-2} ) B. ( 9.8 mathrm{ms}^{-1} ) c. ( 19.6 mathrm{ms}^{-2} ) D. ( 9.8 s^{-2} ) | 11 |

347 | The normal force of an object of mass 5 kg , measured by a force metre is seen to be 50 N. Determine the acceleration due to gravity in ( mathrm{cm} / mathrm{s}^{2} ) A. 1000 B. 100 c. 0.01 D. ( 0 . ) | 11 |

348 | Assertion An astronaut inside a massive spaceship orbiting around the earth will experience a finite but smal gravitational force. Reason The centripetal force necessary to keep the spaceship in orbit around the earth is provided to keep the spaceship in orbit. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

349 | A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is ( V ). Due to the rotation of planet about its axis the acceleration due to gravity ( g ) at equator is ( frac{1}{2} ) of ( g ) at poles. The escape velocity of a particle on the pole of planet in terms of ( V ) A. ( V_{e}=2 V ) B . ( V_{e}=V ) ( mathbf{c} cdot V_{e}=V / 2 ) D. ( V_{e}=sqrt{2} V ) | 11 |

350 | A man of weight mg is moving upwards in a rocket with acceleration 4 g. His apparent weight in side the rocket will be? A. zero B. ( 4 mathrm{mg} ) ( mathrm{c} cdot 5 mathrm{mg} ) D. ( 2 mathrm{mg} ) | 11 |

351 | For moon its mass is ( frac{1}{81} ) of earth’s mass and its diameter is ( frac{1}{3.7} ) of earth’s diameter. If acceleration due to gravity of earth surface is ( 9.8 m / s^{2}, ) then at moon its value is A ( cdot 2.86 m / s^{2} ) B . ( 1.65 m / s^{2} ) ( mathbf{c} cdot 8.65 m / s^{2} ) D. ( 5.16 m / s^{2} ) | 9 |

352 | How much below the surface of the earth does the acceleration due to gravity become ( 70 % ) of its value at the surface of earth? (Take ( boldsymbol{R}=mathbf{6 4 0 0 k m} ) ) | 11 |

353 | A satellite in earth orbit experiences a small drag force as it enters the earth’s atmosphere. Two students were asked consequence of this Student-A : The satellite would slow down as, it spirals towards earth due to work of frictional force. Student-B : The satellite speed up due | 11 |

354 | The figure shows the elliptical orbit of a planet ( P ) about the sun S. The shaded area SCD is a twice shaded area SAB. if ( t_{1} ) is the the time for the planet to move from ( C ) to ( D ) and ( t_{2} ) is the time to move from ( A ) to ( B ), then A ( cdot t_{1}=t_{2} ) ( mathbf{B} cdot t_{1}=2 t_{2} ) ( mathbf{c} cdot t_{1}=4 t_{2} ) ( mathbf{D} cdot t_{1}>t_{2} ) | 11 |

355 | 1 ( g ) force is the force due to gravity on a mass of ( mathbf{A} cdot 1 k g ) в. ( 0.1 k g ) c. ( 0.01 k g ) D. ( 0.001 k g ) | 9 |

356 | An Earth’s satellite is moving in a circular orbit with a uniform speed ( boldsymbol{v} ). If the gravitational force of the Earth suddenly disappears, the satellite will A. vanish into outer space B. continue to move with velocity ( v ) in original orbit c. fall down with increasing velocity. D. fly off tangentially from the orbit with velocity ( v ) | 9 |

357 | 5. Given that acceleration due to gravity varies inversely as the square of the distance from the center of earth, find its value at a height of 64 km from the earth’s surface, if the value at the surface be 9.81 ms-2. Radius of earth = 6400 km. | 11 |

358 | A satellite is launched into a circular orbit of radius ( R ) around the earth. Another second satellite is launched into an orbit of radius ( 1.01 R ). The period of the second satellite is longer than that first by approximately A . ( 0.5 % ) в. ( 1.0 % ) c. ( 1.5 % ) D. 3.0% | 11 |

359 | An astronaut who weighs 162 pounds on the surface of the earth is orbiting the earth at a height above the surface of the earth of two earth radii ( (h=2 R ) where ( R ) is the radius of the earth. How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?) A. 81 pounds B. 40.5 pounds c. 18 pounds D. 54 pounds E. 0 pounds (astronaut is weightless | 11 |

360 | Choose the correct statement: A. All bodies repel each other in this universe B. Our earth does not behave like a magnet C. Acceleration due to gravity is ( 8.9 mathrm{m} / mathrm{s}^{2} ) D. All bodies fall at the same rate in vacuum | 11 |

361 | The kinetic energies of a planet in an elliptical orbit about the Sun, at positions ( A, B ) and ( C ) are ( K_{A}, K_{B} ) and ( K_{C} ) respectively. ( A C ) is the major axis and ( S B ) is perpendicular to ( A C ) at the position of the Sun ( S ) as shown in the figure. Then. A ( cdot K_{B}<K_{A}<K_{C} ) B. ( K_{A}<K_{B}K_{A}>K_{C} ) D. ( K_{A}>K_{B}>K_{C} ) | 11 |

362 | Rockets are lunched in Eastward direction to take advantage of: A. The clear sky on Eastersn side B. The thinner atmosphere on this side c. both A and B D. non of the above | 11 |

363 | A body of mass ( 5 k g ) is cut into two parts of masses (a) ( frac{m}{4} ; frac{3 m}{4} ) (b) ( frac{m}{7} ; frac{5 m}{7} ) (c) ( frac{boldsymbol{m}}{2} ; frac{boldsymbol{m}}{boldsymbol{2}} ) (d) ( frac{boldsymbol{m}}{mathbf{5}} ; frac{boldsymbol{4} boldsymbol{m}}{mathbf{5}} . ) When these two pieces are kept apart by certain distance; In which case the gravitational force acting is maximum? A. In case a B. In case ( c ) c. In case d D. In case b | 9 |

364 | A satellite of mass ( 1000 k g ) is supposed to orbit the earth at a height of ( 2000 k m ) above the earth’s surface. Find the potential energy of the earth-satellite system. | 11 |

365 | State whether true or false. The weight of a freely falling body from a very large height is always constant A. True B. False | 11 |

366 | A satellite is moving in a circular orbit round the earth. If gravitational pull suddenly disappears,then it A. Continuous to move with the same speed along the same path B. Moves with the same velocity tangential to original orbit c. Falls down with increasing velocity. D. comes to rest after moving certain distance along original path. | 9 |

367 | A body of mass ( m ) is moving in a circular orbit of radius ( boldsymbol{R} ) about a planet of mass ( M . ) At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius ( frac{boldsymbol{R}}{longrightarrow} ) ( overline{2} ) and the other mass, in a circular orbit of radius ( frac{3 R}{2} . ) The difference between the final and initial total energies is: A. ( -frac{G M m}{2 R} ) в. ( +frac{G M m}{6 R} ) c. ( frac{G M m}{2 R} ) D. ( -frac{G M m}{6 R} ) | 11 |

368 | At what height, the value of ‘g’ is half that on the surface of the earth of radius ( boldsymbol{R} ? ) A. ( R ) в. ( 2 R ) c. ( 0.414 R ) D. ( 0.75 R ) | 11 |

369 | If ( G ) is the universal gravitation constant and is the uniform density of a spherical planet, then, A. Time period of a planet will be independent of density of the planet B. The shortest period of rotation of the planet will have very high density c. The shortest period of rotation of the planet will have very low density D. The shortest period of rotation of the planet depends on the radius of the planet | 11 |

370 | State Kepler’s third law. | 11 |

371 | Kepler’s third law of planetary motion states that : (Symbols have their usual meaning) A. ( V_{0}=sqrt{R g} ) B . ( overrightarrow{F_{12}}=-overrightarrow{F_{21}} ) ( mathbf{c} cdot r^{2} propto T^{3} ) ( mathbf{D} cdot r^{3} propto T^{2} ) | 11 |

372 | The ratio of the value of ( G ) in ( S ) l units to CGS units is ( mathbf{A} cdot 10^{3}: 1 ) B ( cdot 10^{2}: 1 ) ( mathbf{c} cdot 10^{-2}: 1 ) D. ( 10^{-3}: 1 ) | 11 |

373 | An object takes ( 5 s ) to reach the ground from a height of ( 5 m ) on a planet. What is the value of ( g ) on the planet? | 11 |

374 | Rank the arrangements of masses given in the table below according the force between masses, greatest first. The first column in the table tells the mass of one of the objects in each arrangements, the second column gives the mass of the second object, and the third column gives the distance between the centers of the objects. ( boldsymbol{m}_{1} ) , an a ( m_{2} ) Arrangement 1 M м М 2M 1 Arrangement 2 зм 1 Arrangement 3 1 М A .1,2,3 B. 1,2 and 3 tie c. 1,3,2 D. 3, 2,1 E. 2 and 3 tie, | 11 |

375 | The radius of a planet is 4 times the radius of the earth. The time period of revolution of the planet will be: A . ( 1 y r ) B. 2 ( y r ) c. ( 4 y r ) D. ( 8 y r ) | 11 |

376 | The mass of the moon is about ( 1.2 % ) of the mass of the earth. Compared to the gravitational force that earth exerts on the moon, the gravitational force of the moon exerted on earth: A. Is the same B. Is smaller c. Is greater. D. Varies with its phase | 9 |

377 | A mass ( mathrm{M} ) is broken in two parts: ( mathrm{m} ) and ( (M-m) . ) Relation between ( m ) and ( M s o ) that the force of gravitation between the two parts is maximum is. ( A cdot m M=2 ) в. ( m=frac{M}{2} ) c. ( M=m^{2} ) D. None of these | 11 |

378 | Assertion Newton’s law of gravitation resembles Coulomb’s law of electrical forces. Reason Coulomb’s law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

379 | A bullet is fired vertically upwards with velocity ( v ) from the surface of a spherical planet. When it reaches its maximum heights, its acceleration due to the planet’s gravity is ( 1 / 4 ) th of its value at the surface of the planet. If the escape velocity from the planet is ( boldsymbol{v}_{e s c}=boldsymbol{v} sqrt{boldsymbol{N}}, ) then the value of ( mathrm{N} ) is (ignore energy loss due to atmosphere) | 11 |

380 | On a planet where ( boldsymbol{g}_{text {planet}}=mathbf{0 . 2} boldsymbol{g}_{text {earth}} ) What will be the difference in the height of column filled with mercury in a closed end manometer when the gas is filled withe pressure of ( 2 a t m ) on earth (Assuming:outside pressure to be 1 atm on both planet; Volume of gas remain constant) A . ( 30.4 mathrm{cm} ) в. ( 760 mathrm{cm} ) c. ( 380 c m ) D. 152 ст | 11 |

381 | ENERGY OF AN ORBITING SATELLITE The change in potential energy is: ( ^{A} cdot frac{G M_{E} m}{2 R_{E}} ) в. ( frac{G M_{E} m}{4 R_{E}} ) c. ( frac{G M_{E} m}{8 R_{E}} ) D. ( frac{G M_{E} m}{R_{E}} ) | 11 |

382 | A planet of mass ( m ) moves around the sun of mass ( M ) in an elliptical orbit. The maximum and minimum distances of the planet from the sun are ( r_{1} ) and ( r_{2} ) respectively. The time period of the planet is proportional to: ( mathbf{A} cdot r_{1}^{3 / 2} ) B ( cdot r_{2}^{3 / 2} ) c. ( left(frac{r_{1}+r_{2}}{2}right)^{3 / 2} ) D. ( frac{left(r_{1}-r_{2}right)^{3 / 2}}{2} ) | 11 |

383 | The International Space Station is currently under construction. Eventually, simulated earth gravity may become a reality on the space station. What would the gravitational field through the central axis be like under these conditions? A. zero B. ( 0.25 g ) ( mathrm{c} .0 .5 mathrm{g} ) D. ( 0.75 g ) E . ( 1 g ) | 11 |

384 | A particle would take time ( t_{1} ) to move down a straight tube from the surface of earth (supposed to be homogeneous sphere) to its centre. If gravitational acceleration were to remain constant time would be ( t_{2} ). The ratio ( t / t^{prime} ) will be A ( cdot frac{pi}{2 sqrt{2}} ) в. ( frac{pi}{2} ) c. ( frac{2 pi}{3} ) D. ( frac{pi}{sqrt{3}} ) | 11 |

385 | Correct form of gravitational law is: A ( cdot vec{F}=-frac{G m_{1} m_{2}}{r^{2}} ) В ( cdot vec{F}=-frac{G m_{2} m_{1}}{r^{2}} ) c. ( vec{F}=-frac{G m_{1} m_{2}}{r^{2}} hat{r} ) D・ ( vec{F}=-frac{G m_{1} m_{2}}{r^{3}} vec{r} ) | 11 |

386 | A body is lying on the surface of earth.Suppose that the earth suddenly loses its power of attraction, then A. the weight of body will become zero B. the weight of body will become infinite c. the mass of the body will become zero D. the body will vanish in air | 11 |

387 | Time period of simple pendulum in a satellite is A . Infinite B. Zero c. 2 sec D. Cannot be calculated | 11 |

388 | If the mass of a body is ( M ) on the surface of the earth, the mass of the same body on the surface of the moon is A. ( M / 6 ) в. ( M ) ( c cdot 6 M ) D. zero | 11 |

389 | What is the minimum energy required to launch a satellite of mass ( m ) from the surface of a planet of mass ( M ) and radius ( R ) in a circular orbit at an altitude of ( 2 R ? ) A ( cdot frac{2 G m M}{3 R} ) в. ( frac{G m M}{2 R} ) c. ( frac{G m M}{3 R} ) D. ( frac{5 G m M}{6 R} ) | 11 |

390 | The acceleration due to gravity ( g ) and density of the earth ( p ) are related by which of the following relations? (Here ( G ) is the gravitational constant and ( R ) is the radius of the earth) A ( cdot p=frac{4 pi}{3 G R d} ) в. ( _{p}=frac{3 g}{4 pi G R} ) c. ( _{p}=frac{3 G}{4 pi G R} ) D. ( p=frac{4 pi G R}{3 G} ) | 11 |

391 | The escape velocity of a particle of mass ( m ) varies as: ( mathbf{A} cdot m^{2} ) в. ( m ) c. ( m^{0} ) D. ( m^{-1} ) | 11 |

392 | The acceleration due to gravity: A. has the same value everywhere is space B. has the same value everywhere on the earth C. varies with the latitude on the earth D. is greater on the moon due to its smaller diameter | 11 |

393 | Find the gravitational force between two atoms in a hydrogen molecule. Given that ( G=6.67 times 10^{-11} N m^{2} k g^{-2} ) and mass of hydrogen atom ( 1.67 times 10^{-27} k g ) and the distance between the two atoms1 ( ^{circ} A . ) The answer is ( 1.86 times ) ( 10^{-x y} N ) then ( x+y= ) | 11 |

394 | A small mass ( m ) is moved slowly from the surface of the earth to a height ( h ) above the surface. The work done (by an external agent) in doing this is This question has multiple correct options A. ( m g h, ) for all values of ( h ) B. ( m g h, ) for ( h<<R ) c. ( frac{1}{2} ) mgR, for ( h=R ) D. ( -frac{1}{2} ) mgR, for ( h= ) | 11 |

395 | If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct? A. Time period of a simple pendulum on the Earth would decrease B. Raindrops will fall faster c. ‘g’on the Earth will not change D. Walking on the ground would become more difficult | 11 |

396 | Depth from the surface of the earth at which is acceleration due to gravity is ( 25 % ) of acceleration due to gravity at the surface A. ( 1200 mathrm{km} ) B. 4000 km c. ( 3600 mathrm{km} ) D. ( 4800 mathrm{km} ) | 11 |

397 | Name two force in nature that have longest and shortest range | 9 |

398 | Earth radius is ( boldsymbol{R} ) and spin angular velocity of Earth is ( omega . ) At what height above the North pole the acceleration due to gravity will be same as that at the equation? ( (g ) is acceleration due to gravity at North pole). | 11 |

399 | The gravitational potential difference between the surface of a planet and a point ( 20 m ) above the surface is 2Joule/Kg. If the gravitational field is uniform then the work done in carrying a ( 5 K g ) body to a height of ( 4 m ) above the surface is A . 2 Joule в. 20Joule c. 40 Joule D. 10 Joule | 11 |

400 | Net torque on the planet is A. Constant at all points B. Zero at all point c. Maximum at ( A ) D. Minimum at ( D ) | 11 |

401 | The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity : A. will be directed towards the centre but not the same everywhere B. will have the same value everywhere but not directed towards the centre c. will be same everywhere in magnitude directed towards the centre D. cannot be zero at at point | 11 |

402 | Escape velocity when a body of mass ( m ) is thrown vertically from the surface of the earth is ( v, ) what will be the escape velocity of another body of mass ( 4 m ) if thrown vertically ( A ) B . ( 2 v ) c. ( 4 v ) D. None of these | 11 |

403 | If the gravitational potential on the surface of earth is ( V_{0} ) then potential at a point at height half of the radius of earth is A ( cdot frac{V_{0}}{2} ) в. ( frac{2}{3} V_{0} ) c. ( frac{V_{0}}{3} ) D. ( frac{3 V_{0}}{2} ) | 11 |

404 | On the earth, a Sumo of ( 420 mathrm{kg} ) is checking his reading on a spring balance. To have the same reading of spring balance on the moon, how many Sumos of mass ( 420 mathrm{kg} ) each should stand on it. Explain. ( left(g=30 mathrm{m} mathrm{s}^{-2}right) ) ( A cdot 6 ) B. 12 ( c cdot 18 ) D. | 9 |

405 | Figure shows position and velocities of two particles moving under mutual gravitational attraction in space at time ( t=0 . ) The position of centre of mass after one second is : ( mathbf{A} cdot x=4 m ) B . ( x=6 m ) ( mathbf{c} cdot x=8 m ) D. ( x=10 m ) | 11 |

406 | Two identical solid copper spheres of radius ( R ) are placed in contact with each other. The gravitational attraction between them is proportional to ( mathbf{A} cdot R^{2} ) B. ( R^{-2} ) ( c cdot R^{-4} ) D. ( R^{4} ) | 11 |

407 | A spaceship moves in a circular orbit of radius ( 7200 mathrm{km} ) round the earth. How far does it travel while sweeping an angle of ( 100^{circ} ? ) | 11 |

408 | Which of the following is true for universal law of gravitation? (1) It acts on all the objects irrespective of their nature, shape and size (2) ( boldsymbol{F} propto boldsymbol{M} times boldsymbol{m} ) (3) It acts along the line joining the centers of the two objects. (4) ( boldsymbol{F} propto frac{1}{d^{2}} ) A . a and c B. b and d ( c cdot a, b ) and ( d ) D. All of the above | 11 |

409 | At what height from the surface of earth will the value of ( g ) be reduced by ( 36 % ) from the value at the surface? ( boldsymbol{R}= ) ( 6400 k m ) A . ( 400 k m ) B. ( 800 k m ) ( c .1600 k m ) D. 3200km | 11 |

410 | A body of mass ( m ) is moving in a circular orbit of radius ( boldsymbol{R} ) about a planet of mass ( M . ) At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius ( frac{boldsymbol{R}}{longrightarrow} ) ( overline{2} ) and the other mass, in a circular orbit of radius ( frac{3 R}{2} . ) The difference between the final and initial total energies is: A. ( -frac{G M m}{2 R} ) в. ( +frac{G M m}{6 R} ) c. ( frac{G M m}{2 R} ) D. ( -frac{G M m}{6 R} ) | 11 |

411 | The radius of a planet is ( R_{1} ) and ( a ) satellite revolves around it in a radius ( mathrm{R} ) 2 Time period of revolution is ( T . ) Find the acceleration due to gravity. ( ^{mathbf{A}} cdot frac{4 pi^{2} R_{2}^{3}}{R_{1}^{2} T^{2}} ) B. ( frac{4 pi^{2} R_{2}^{2}}{R_{1} T^{2}} ) ( ^{mathrm{c}} cdot frac{2 pi^{2} R_{2}^{3}}{R_{1} T^{2}} ) D. ( frac{4 pi^{2} R_{2}}{T^{2}} ) | 11 |

412 | The angular velocity of the earth’s rotation about its axis is ( omega . ) An object weighed by a spring balance gives the same reading at the equator as at height ( h ) above the poles, the value of ( h ) will be: ( ^{mathrm{A}} cdot frac{omega^{2} R^{2}}{g} ) В. ( frac{omega^{2} R^{2}}{2 g} ) c. ( frac{2 omega^{2} R^{2}}{g} ) D. ( frac{2 omega^{2} R^{2}}{3 g} ) | 11 |

413 | The time period of an earth satellite in circular orbits is independent of A. both the mass and radius of the orbit B. radius of its orbit c. the mass of the satellite D. neither the mass of the satellite nor the radius of its orbit | 11 |

414 | Obtain an expression for acceleration due to gravity at a height ( h ) above the earth’s surface. | 11 |

415 | Can a pendulum vibrate in an artificial satellite? | 11 |

416 | Find the work done to take a particle of mass ( mathrm{m} ) from surface of the earth to a height equal to ( 2 R ) ( mathbf{A} cdot 2 m g R ) в. ( frac{m g R}{2} ) c. ( 3 m g R ) D. ( frac{2 m g R}{3} ) | 11 |

417 | The relationship between acceleration due to gravity ( (g) ) and universal gravitational constant( ( G ) ) may be represented as: ( (M text { and } R ) are the mass and radius of the earth respectively A. ( G=frac{g M}{R^{2}} ) В. ( g=frac{G M}{R^{2}} ) c. ( g=frac{G}{R^{2}} ) D. None of these | 11 |

418 | Solve: A sphere of mass ( 10 mathrm{kg} ) is attracted by another sphere of mass ( 150 mathrm{kg} ), with a force equal to ( 1.28 times 10^{-6} N, ) when their centers are separated by a distance of ( 0.28 mathrm{m} . ) Calculate the gravitational constant. | 11 |

419 | Sl unit of ( G ) is ( N m^{2} k g^{-2} . ) Which of the following can also be used as the Sl unit of G? A ( cdot m^{3} k g^{-1} s^{-2} ) B . ( m^{2} k g^{-2} s^{-1} ) ( mathbf{c} cdot m k g^{-3} s^{-1} ) D. ( m^{2} k g^{-3} s^{-2} ) | 11 |

420 | The escape velocity of a body thrown vertically upwards from the surface of earth is ( 11.2 mathrm{Km} / mathrm{s} . ) If it is thrown in a direction making an angle of ( 30^{0} ) from the vertical, the new escape velocity will be ( mathbf{A} cdot 5.6 mathrm{Km} / mathrm{s} ) B. ( 11.2 mathrm{Km} / mathrm{s} ) c. ( 11.2 times sqrt{2} mathrm{km} / mathrm{s} ) D. ( _{11.2} times frac{sqrt{3}}{2} mathrm{km} / mathrm{s} ) | 11 |

421 | The angular velocity of rotation of a star (mass ( mathrm{M} ) and radius ( mathrm{R} ) ), such that the matter will start escaping from its equator is: A ( cdot sqrt{frac{2 G R}{M}} ) в. ( sqrt{frac{2 G M}{R^{3}}} ) c. ( sqrt{frac{2 G M}{R}} ) D. ( sqrt{frac{2 G M^{2}}{R}} ) | 11 |

422 | An artificial satellite moving in a circular orbit around the earth has a total energy ( boldsymbol{E}_{0} . ) Its potential energy is A. ( -E_{0} ) в. ( E_{0} ) c. ( 2 E_{0} ) D. ( -2 E_{0} ) | 11 |

423 | Kepler’s laws of planetary motion provides information about: A. areal velocity of a planet B. nature of motion of a planet C. ratio of time periods of two planets D. all the above | 11 |

424 | The radius and acceleration due to gravity of the moon are ( frac{1}{4} ) and ( frac{1}{5} ) that of the earth, the ratio of the mass of the earth to mass of the moon is : ( mathbf{A} cdot 1: 80 ) B. 80: 1 c. 1: 20 D. 20:1 | 11 |

425 | Two blocks ( A ) and ( B ) of masses ( M_{A} ) and ( M_{B} ) respectively, are located ( 1.0 m ) apart on a horizontal surface. The coefficient of static friction ( mu_{s} ) between the block and the surface is ( 0.50 . ) Block ( A ) is secured to the surface and cannot move, what is the minimum mass of Block ( A ) that provides enough gravitational attraction to move Block B? The universal gravitation constant is ( 6.67 times 10^{-11} N m^{2} / k g^{2} .(g= ) ( 9.8 m s^{-2} ) A ( cdot 7.5 times 10^{9} k g ) в. ( 7.3 times 10^{16} k g ) c. ( 14.7 times 10^{11} k g ) D. The problem cannot be solved without knowing the mass of Block ( B ) | 11 |

426 | Acceleration of particle moving rectilinearly is ( a=4-2 x ) (where ( x ) is position in meter and ( a ) in ( m s^{-2} ) ). It is at instantaneous rest at ( x=0 . ) At what position ( x ) (in meter) will the particle again come to instantaneous rest? | 11 |

427 | If the earth were to suddenly contract to ( frac{1}{m} ) th of its present radius without any ( boldsymbol{n} ) change in its mass then the duration of the new day will be close to ( ^{mathrm{A}} cdot frac{24}{n} ) hour B. ( 24 n ) hour c. ( frac{24}{n^{2}} ) hour D. ( 24 n^{2} ) hour | 11 |

428 | Calculate the gravitational field intensity and potential at the centre of the base of a solid hemisphere of mass ( mathrm{m}, ) radius ( mathrm{R} ) | 11 |

429 | Journey in a train is adventurous particularly when you have a seat. The girl sitting near window ate a banana and dropped the peel from the window. Her co-passenger looking through the window found that it dropped vertically down and touched the ground in ( 0.2 s ) After sometime she requested her sister sitting on the upper berth to drop a chocolate bar.The sister dropped the bar, but it fell in front of the girl instead of reaching her hand. She was angry but the co-passenger calmed her by saying that she dropped exactly in line of your hand but as the train is accelerating it did not reach you and fell in front of you. If a projectile has velocity greater than escape velocity which trajectory it will follow A. elliptic B. hyperbola c. vertical straight D. parabolic | 11 |

430 | Assertion If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. Reason Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

431 | Two planets ( A ) and ( B ) have the same average density. Their radii ( boldsymbol{R}_{A} ) and ( boldsymbol{R}_{B} ) are such that ( boldsymbol{R}_{boldsymbol{A}}: boldsymbol{R}_{boldsymbol{R}}=boldsymbol{3}: boldsymbol{1} ) If ( boldsymbol{g}_{A} ) and ( g_{B} ) are the acceleration due to gravity at the surfaces of the planets, the ( g_{A}: g_{B} ) equals A . 3: 1 B. 1: 3 c. 9: 1 D. 1: 9 E . ( sqrt{3}: 1 ) | 11 |

432 | What the decrease in weight ofa body of mass 600 kg when it is taken in a mine of depth ( 5000 mathrm{m} ) ? [Radius of earth a ( 6400 mathrm{km}, mathrm{g}=9.8 mathrm{m} / mathrm{s}^{2} ) | 11 |

433 | A geostationary satellite is orbiting the earth at a height of ( 5 R ) above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of ( 2 mathrm{R} ) from the surface of the earth is: A ( cdot frac{6}{sqrt{2}} ) B. 5 c. 10 D. ( 6 sqrt{2} ) | 11 |

434 | Pick out the wrong statement from the following A. The Sl unit of universal gravitational constant is ( N m^{2} k g^{-2} ) B. The gravitational force is a conservative force C. The force of attraction due to a hollow spherical shell of uniform density on a point mass inside it is zero D. The centripetal acceleration of the satellite is equal to acceleration due to gravity E . Gravitational potential energy ( =frac{text { gravitation potential }}{text { mass of the body }} ) | 11 |

435 | An astronaut whose mass is ( 84 mathrm{kg} ) on earth will have a mass of approximately ( 14 mathrm{kg} ) on the moon. A. True B. False | 9 |

436 | ( R ) and ( r ) are the radii of the Earth and the Moon respectively and ( rho_{e} ) and ( rho_{m} ) are the densities of the Earth and Moon respectively. The ratio of acceleration due to gravity on the surface of the Earth to the Moon is: A ( cdot frac{R}{r} cdot frac{rho_{e}}{rho_{m}} ) в. ( frac{r}{R} cdot frac{rho_{e}}{rho_{m}} ) c. ( frac{r}{R} cdot frac{rho_{m}}{rho_{e}} ) D. ( frac{R}{r} cdot frac{rho_{m}}{rho_{e}} ) | 11 |

437 | A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate (i) The maximum height to which it rises. ( (i i) ) The total time it takes to return to the surface of the earth. | 11 |

438 | Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to ( r^{5 / 2}, ) then the square of the time period will be proportional to. A ( cdot r^{3} ) в. ( r^{2} ) ( c cdot r^{2.5} ) D. ( r^{3.5} ) | 11 |

439 | State whether the given statement is True or False : The value of ( G ) is high if the radius of the body is more and less if radius is less. A . True B. False | 11 |

440 | Assertion Smaller the orbit of the planet around the sun, shorter is the time it takes to complete one revolution Reason According to Kepler’s third law of planetary motion, square of time period is proportional to cube of mean distance from sun A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

441 | If ( M_{E} ) is the mass of the earth and ( R_{E} ) its radius, the ratio of the acceleration due to gravity and the gravitational constant is: ( ^{text {A }} cdot frac{R_{E}^{2}}{M_{E}} ) в. ( frac{M_{E}}{R_{E}^{2}} ) c. ( M_{E} R_{E}^{2} ) D. ( frac{M_{E}}{R_{E}} ) | 11 |

442 | The escape velocity on the surface of a planet is ( V_{e} ) what would be the escape velocity on the planet having the same radius but mass 4 times that of it. ( A cdot 2 V_{e} ) B. ( 4 V_{e} ) c. ( V_{c} ) ( D cdot frac{V_{c}}{2} ) | 11 |

443 | Escape velocity at surface of earth is 11.2Km/s. Escape valocity from a planet whose mass is the same as that of earth and radius ( 1 / 4 ) that of earth, is? A ( .2 .8 mathrm{km} / mathrm{s} ) B. ( 15.6 mathrm{km} / mathrm{s} ) c. ( 22.4 mathrm{km} / mathrm{s} ) D. ( 44.8 mathrm{km} / mathrm{s} ) | 11 |

444 | f a satellite is revolving around a planet of mass ( mathrm{M} ) in an elliptical orbit of semimajor axis a. Show that the orbital speed of the satellite when it is at a distance r from the focus will be given by ( boldsymbol{v}^{2}=boldsymbol{G} boldsymbol{M}left[frac{boldsymbol{2}}{boldsymbol{r}}-frac{mathbf{1}}{boldsymbol{a}}right] ) | 11 |

445 | The average acceleration due to gravity is ( 8.9 mathrm{ms}^{-2} ) A. True B. False | 11 |

446 | Two satellites ( A ) and ( B ) revolve around a planet in two coplanar circular orbits in the same sense with radii ( 10^{4} mathrm{km} ) and ( 2 times 104 mathrm{km} ) respectively. Time period of ( A ) is 28 hours. What is time period of another satellite? | 11 |

447 | How is the acceleration due to gravity on earth surface related to the mass ( M ) and radius ( R ) of earth? A ( cdot g=frac{G}{M R^{2}} ) в. ( g=frac{M}{G R^{2}} ) c. ( _{g}=frac{G M}{R} ) D. ( g=frac{G M}{R^{2}} ) | 11 |

448 | A pendulum beats seconds on the earth. Its time period on a stationary satellite of the earth will be A. zero B. ( 1 s ) ( c cdot 2 s ) D. Infinity | 11 |

449 | If the earth stops rotating.then the value of acceleration due to gravity at a latitude ( 45^{circ} ) will increases by | 11 |

450 | Two spheres each of mass ( 10^{5} k g ) and radius ( 10 m ) are kept in contact. Find the force of gravitation acting between them. A ( cdot 5.67 times 10^{-3} N ) N ( .5 .67 times 10^{-3} .6 times 10^{-3} ) в. ( 6.67 times 10^{-3} N ) c. ( 3.67 times 10^{-3} N ) D. 2.67 ( times 10^{-3} N ) | 11 |

451 | The weight of a body on the surface of the moon is ( frac{1}{6} t h ) of that on the earth’s surface. It is because acceleration due to gravity on the surface of the moon is six times that on the surface of the earth. A . True B. False | 9 |

452 | What is the nature of relation betweenthe kinetic energy ( left(mathbf{E}_{mathbf{k}}right) ) and their orbitalradius (r) of the satellites revolvingaround the Earth? ( mathbf{A} cdot E_{k} propto 1 ) B . ( E_{k} propto frac{1}{r} ) ( mathrm{c} cdot E_{k} propto r^{2} ) D. ( E_{k} propto frac{1}{r^{2}} ) | 11 |

453 | If the earth is at one fourth of its present distance from the sun, the duration of the year will be A. Half the present year B. One eighth of the present year c. one fourth of the present year D. One sixth of the present year | 11 |

454 | A satellite is changes it orbit from radius of ( mathrm{R} ) to radius of ( 2 mathrm{R} ). If its initial kinetic energy is ( K_{1} ) then calculate the new kinetic energy. A ( cdot frac{K_{1}}{4} ) в. ( frac{K_{1}}{2} ) c. ( K_{1} ) D. ( 2 K_{1} ) E ( .4 K_{1} ) | 11 |

455 | If the weight of a body on the earth is 12 Newtons (N), its weight on the moon will be: A. २N B. 24 kg c. 12N D. ( 12 mathrm{kg} ) | 9 |

456 | The work done by external agent to shift a point mass from infinity to the centre of earth is : ( mathbf{A} cdot=0 ) ( mathbf{B} cdot>0 ) ( c cdot<0 ) ( mathrm{D} cdot<0 ) | 11 |

457 | Calculate the value of ( g ) on the surface of planet if the planet has ( 1 / 500 ) the mass and ( 1 / 15 ) the radius of the Earth в. ( 1.6 m / s_{2} ) ( mathrm{c} cdot 2.4 mathrm{m} / mathrm{s}_{2} ) D. ( 4.5 m / s_{2} ) E ( .7 .1 mathrm{m} / mathrm{s}_{2} ) | 11 |

458 | In the Newton’s gravitational law, ( boldsymbol{F}= ) ( frac{G M m}{d^{2}}, ) the quantity ( G ) A. depends on the value of ( g ) at the place of observation B. is used only when the earth is one of the two masses c. is greatest at the surface of the earth D. is universal constant in nature | 11 |

459 | Mass of the earth has been determined through A ( cdot ) use of Kepler’s ( frac{T^{2}}{R^{3}} ) constancy law B. sampling the density of earth’s crust and using earth’s radius. C. Cavendish’s determination of G and using earth’s radius and ( g ) at its surface. D. use of periods of satellites at different heights above earth’s surface. | 11 |

460 | If ( g ) is the acceleration due to gravity on the earth’s surface, the gain of the potential energy of an object of mass ( boldsymbol{m} ) raised from the surface of the earth to a height equal to the radius ( R ) of the earth will be : A. ( 2 m g R ) в. ( m g R ) c. ( frac{1}{2} m g R ) D. ( frac{1}{4} m g R ) | 11 |

461 | The value of acceleration due to gravity: A. is same on equator and poles B. is least on poles ( mathrm{c} ). is least on equator D. increases from pole to equator | 11 |

462 | Which of the following statements corresponds to Kepler’s laws of planetary motion? A. A planet moves around the sun in a circular orbit B. A planet moves around the sun in an elliptical orbit with the sun at the geometrical centre c. A planet moves around the sun in an elliptical orbit with the sun at the focus D. A planet moves around the sun in an elliptical orbit with uniform speed | 11 |

463 | A particle hanging from a massless spring stretches it by ( 2 c m ) at the eath’s surface. How much will the same particle stretch the spring at a height of ( 2624 K m ) from the surface of the earth? (Radius of the earth ( =6400 K m) ) ( A cdot 1 c m ) B. ( 2 c m ) ( c .3 c m ) D. ( 4 c m ) | 11 |

464 | A satellite is launched into a circular orbit of radius r around the earth. ( mathbf{A} ) second satellite is launched into an orbit of radius ( 1.01 mathrm{r} ). The period of the second satellite is larger than that of first one by approximately. ( A cdot 0.5 % ) B . 1.0 % c. ( 1.5 % ) D. 3.0 % | 11 |

465 | Value of ( g ) on the surface of earth is ( 9.8 m / s^{2} . ) Find acceleration due to gravity at depth ( h=frac{R}{2} ) from the surface ( (boldsymbol{R}= ) radius of earth) | 11 |

466 | Suppose gravitational force between two masses were to be given by ( boldsymbol{F}= ) ( k frac{sqrt{m_{1} m_{2}}}{d^{3}} ) where ( k ) is some constant two equal masses attract each other with a certain force when the distance is d. If each of the masses is doubled, than what value the distance between them must be maintained for the force to remain the same as earlier? A. ( sqrt[3]{3 d} ) B. “3/3d ( c cdot sqrt[13]{2 d} ) D. ( sqrt[3]{2 d} ) | 11 |

467 | A (nonrotating) star collapses onto itself from an initial radius ( mathrm{R}_{i} ) with its mass remaining unchanged. Which curve in figure best gives the gravitational acceleration ( a_{g} ) on the surface of the star as a function of the radius of the star during the collapse? 4 B. ( c ) D. | 11 |

468 | A lead sphere of mass ( 20 k g ) has the same diameter as an aluminium sphere of mass ( 72 k g ). The spheres are simultaneously dropped from a tower. When they are ( 10 m ) from the ground, they have identical (neglect air resistance): A. kinetic energy B. potential energy c. momentum D. acceleration | 11 |

469 | The distance between the two point masses ( boldsymbol{m}_{1} ) and ( boldsymbol{m}_{2} ) is d. Now, the distance between them is reduced by two-thirds, Calculate by which factor new gravitational force would be change? A. It increases by a factor of 9 B. It increases by a factor of ( frac{4}{9} ) c. It increases by a factor of 3 D. It decreases by factor of 9 E. It decreases by a factor of 3 | 11 |

470 | A man in a balloon rising vertically with an acceleration of ( 4.9 m / s e c^{2} ) releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reaches by the ball is ( (g= ) ( mathbf{9 . 8 m} / boldsymbol{s e c}^{2} ) A ( .14 .7 m ) B. ( 19.6 m ) ( mathrm{c} .9 .8 mathrm{m} ) D. ( 24.5 m ) | 11 |

471 | A particle of mass ( mathrm{M} ) is placed at origin and a small mass ( mathrm{m} ) is placed at ( mathrm{A}, ) at a distance of ( r ) from M. A force F is applied to ( m ) to make it move from ( A ) to a nearby point B. When the force becomes zero, it is observed that the mass m moves from B back to A. This is due to the reason A. Potential of B is larger than potential of A B. objects starts moving in gravitational field until constant potential difference exist c. The line B to A is equipotential surface D. The mass moves from B to A, since A is nearer to origir | 11 |

472 | If the radius of the earth is reduced by ( 1 % ) keeping the mass constant. The escape velocity will : A. increase by ( 0.5 % ) B. decrease by ( 0.5 % ) c. decrease by ( 11 % ) D. remain same | 11 |

473 | Two lead spheres of ( 20 mathrm{cm} ) and ( 2 mathrm{cm} ) diameter are placed with their centres 1.0 ( m ) apart. Calculate the force of attraction between the two spheres. The radius of the earth is ( 6.37 times 10^{6} m ), its density is ( 5.51 times 10^{3} k g / m^{2} ) and relative density of lead is 11.5 | 11 |

474 | A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be – A. ( mathrm{mg} ) २R в. ( frac{2}{3} m g R ) c. ( 3 mathrm{mgR} ) D. ( frac{1}{3} m g R ) | 11 |

475 | Gravitational unit of force produce an acceleration in a body equal to ( A cdot g ) B. 0 c. ( 2 g ) D. unit value | 9 |

476 | A spherical planet, far out in space, has a mass ( M_{0} ) and diameter ( D_{0} . ) A particle of mass ( m ) falling freely near the surface of this planet will experience acceleration due to gravity which is equal to: A ( cdot frac{G M_{0}}{left(D_{0}right)^{2}} ) в. ( frac{4 m G M_{0}}{left(D_{0}right)^{2}} ) c. ( frac{4 G M_{0}}{left(D_{0}right)^{2}} ) D. ( frac{G m}{left(D_{0}right)^{2}} ) | 11 |

477 | A planet revolves around the sun in an elliptical orbit of eccentricity e. If T is the time period of the planet, then the time spent by the planet between the ends of the minor axis and major axis close to the sun is A ( cdot frac{T pi}{2 e} ) B ( cdot Tleft(frac{2 e}{pi}-1right) ) c. ( frac{T e}{2 pi} ) D ( cdot Tleft(frac{1}{4}-frac{e}{2 pi}right) ) | 11 |

478 | The gravitational force acting on a particle of ( 1 g ) due to a similar particle is equal to ( 6.67 times 10^{-11} ). Calculate the seperation between the particles. | 11 |

479 | On doubling the distance between two masses the gravitational force between them will A. Remain unchanged B. Become one-fourth c. Become half D. Become double | 11 |

480 | The gravitational force of attraction between two bodies at a certain distance is ( 10 mathrm{N} ). If the distance between them is doubled, the force of attraction: A. decreases by ( 50 % ) B. decreases by ( 75 % ) C. increases by ( 50 % ) D. increases by ( 75 % ) | 11 |

481 | What is the escape velocity from the surface of the earth of radius ( R ) and density ( rho ? ) ( ^{text {A }} cdot 2 R sqrt{frac{2 pi rho G}{3}} ) в. ( 2 sqrt{frac{2 pi rho G}{3}} ) c. ( 2 pi sqrt{frac{R}{g}} ) D. ( sqrt{frac{2 pi G rho}{R^{2}}} ) | 11 |

482 | A satellite of mass ( m ) moves along an elliptical path around the earth. The areal velocity of the satellite is proportional to A . ( m ) B. ( m^{-1} ) ( c cdot m^{0} ) ( D cdot m^{frac{1}{2}} ) | 11 |

483 | Suppose a planet exists whose mass and radius both are half that of the earth The acceleration due to gravity on the surface of this planet will be double ( ? ) | 11 |

484 | It is found that the speed of the earth around the sun increases when it is close to the sun. A. Angular velocity of the earth is constant. B. Areal velocity of the earth is not constant. c. Areal velocity of the earth is constant D. None of these. | 11 |

485 | A body of mass ( m ) falls from rest through a height ( h ) under gravitation acceleration ( g ) and is then brought to rest by penetrating through a depth ( d ) into some sand. The average deceleration of the body during penetration into sand is A ( frac{g h^{2}}{d^{2}} ) в. ( frac{g h^{2}}{2 d^{2}} ) c. ( frac{g h}{d} ) D. ( frac{g d}{h} ) | 11 |

486 | The time period of a simple pendulum at the center of the earth is: A . zero B. infinite c. less than zero D. none of these | 11 |

487 | When ( A ) is given its first impulse at the moment: ( A . A, B ) and centre of earth are in same straight line B. ( B ) is ahead of ( A ) angularly ( mathrm{c} . B ) is behide ( A ) angularly D. None of these | 11 |

488 | The force of attraction between two bodies at a certain separation is ( 10 N ) What will be the force of attraction between them if the separation between them is reduced to half? ( mathbf{A} cdot 2.5 N ) B. ( 5 N ) ( c .20 N ) D. ( 40 N ) | 11 |

489 | f ( r_{2}=3 r_{1} ) and time period of revolution for ( B ) be ( T ) than time taken by ( A ) in moving from position 1 to position 2 is : ( ^{A} cdot frac{sqrt{3}}{sqrt{2}} ) 3. ( T frac{sqrt{3}}{2} ) c. ( frac{T sqrt{2}}{3 sqrt{3}} ) D. ( frac{T sqrt{2}}{3} ) | 11 |

490 | The gravitational force between two bodies is decreased by ( 36 % ) when the distance between them is increased by ( 3 m . ) The initial distance between them is: A. ( 6 m ) в. ( 9 m ) ( c .12 m ) D. ( 15 mathrm{m} ) | 11 |

491 | Orbital speed of an artificial satellite very close to earth’s surface is V. Its orbital speed at a height equal to three times the radius of the earth from the earth’s surface is: ( A cdot v ) B. v/2 ( c cdot 2 v ) ( D cdot v / 4 ) | 11 |

492 | If ( R ) is the radius of a planet, ( g ) is the acceleration due to gravity then find the mean density of the planet A ( cdot frac{3 g}{4 G pi R} ) в. ( frac{3 g}{8 G pi R} ) c. ( frac{2 g}{4 G pi R} ) D. ( frac{6 g}{4 G pi R} ) | 9 |

493 | A sky laboratory of mass ( 2 times 10^{3} K g ) is raised from a circular orbit of radius ( 2 mathrm{R} ) to a circular orbit of radius ( 3 mathrm{R} ). The work done is (approximately): ( mathbf{A} cdot 10^{16} J ) В. ( 2 times 10^{10} J ) ( mathbf{c} cdot 10^{6} J ) D. ( 3 times 10^{10} J ) | 11 |

494 | How much the surface of earth does the acceleration due to gravity reduce by ( 36 % ) of its value on the surface of earth? Radius of earth ( =mathbf{6 4 0 0 k m} ) | 11 |

495 | If the weight of a body on the surface of the moon is ( 100 mathrm{N} ), what is its mass? ( left.=1.6 mathrm{ms}^{-2}right) ) ( A cdot 160 mathrm{kg} ) B. 62.5 kg ( c cdot 6.25 mathrm{kg} ) D. 625 kg | 9 |

496 | State the Kelper’s law which is represented by the relation ( r^{3} propto T^{2} ) | 11 |

497 | When will multiple objects of different nature, shape, size etc fall from the same height at the same rate? A. In the presence of vaccum B. on the poles c. on the equator D. None of the above | 11 |

498 | Acceleration due to gravity – – depth from the surface of the earth. A. Decreases B. Increases c. Remains constant D. Data insufficient | 11 |

499 | If value of acceleration due to gravity changes from one place to another, which of the following force will undergo a change? A. Viscous force B. Buoyant force c. Magnetic force D. All of the above | 11 |

500 | Choose the correct statement. A. All bodies repel each other in this universe B. Our earth does not behave like a magnet C . Acceleration due to gravity is ( 8.9 mathrm{m} / mathrm{s}^{2} ) D. All bodies have the same acceleration due to gravity at the surface of the earth | 11 |

501 | A particle hanging from a spring stretches it by ( 1 mathrm{cm} ) at earth’s surface. Radius of earth is ( 6400 k m . ) At a place ( 800 k m ) above the earths surface, the same particle will stretch the spring by A ( .0 .79 mathrm{cm} ) B. ( 1.2 mathrm{cm} ) ( c .4 c m ) D. ( 17 mathrm{cm} ) | 11 |

502 | ( mathbf{1} boldsymbol{g} boldsymbol{f}= ) A. 980 dyne B. 98 dyne c. 9.8 dyne D. 0.98 dyne | 9 |

503 | Derivation for weight pf an object on the surface of the moon. | 9 |

504 | A body is suspended from a spring balance kept in a satellite. The reading of the balance is ( W_{1}, ) when the satellite goes in an orbit of radius ( boldsymbol{R} ) and is ( boldsymbol{W}_{2} ) when it goes in an orbit of radius ( 2 R ) A. ( W_{1}=W_{2} ) в. ( W_{1}W_{2} ) D. ( W_{1} neq W_{2} ) | 11 |

505 | Every planet revolves around the sun in a/an orbit. A. elliptical B. circular c. parabolic D. none of these | 11 |

506 | A spring balance whose maximum extension of its spring is ( 20 mathrm{cm} ) can sustain a maximum load of ( 20 k g_{w t} ) within its elastic limit on the surface of the earth. Now the same balance is taken to the moon. Given that gearth ( =6 g_{text {moon }}, ) what is the maximum mass of the load that can be attached to the balance to have half its maximum extension? A . 76 B. 65 c. 60 D. 55 | 11 |

507 | A mass ( M ) at rest is broken into two pieces having masses ( m ) and ( (M-m) ) The two masses are then separated by a distance ( r . ) The gravitational force between them will be the maximum when he ratio of the masses ( [boldsymbol{m}:(boldsymbol{M}- ) ( boldsymbol{m}) ) of the two parts is A . 1: B. 1: 2 ( c cdot 1: 3 ) D. 1: 4 | 11 |

508 | The ratio of the radii of planets ( A ) and ( B ) is ( K_{1} ) and ratio of accelerations due to gravity on them is ( K_{2} ) The ratio of escape velocities from them will be: A. ( K_{1} K_{2} ) B. ( sqrt{K_{1} K_{2}} ) c. ( sqrt{frac{K_{1}}{K_{2}}} ) D. ( sqrt{frac{K_{2}}{K_{1}}} ) | 11 |

509 | What is value of gravitational acceleration at the center of the earth? ( mathbf{A} cdot 9.8 m s^{2} ) B. zero c. infinite D. ( 6.67 times 10^{-11} mathrm{ms}^{-2} ) | 11 |

510 | The Orbit of a planet moving around the sun Refer image. Observe the given figure showing the orbit of a planet moving around the Sun and write the three laws related to it: | 11 |

511 | The acceleration due to gravity A. Has the same value everywhere in space B. Has the same value everywhere on the earth C. varies with the latitude on the earth D. is greater on the moon due to its smaller diameter | 11 |

512 | From the centre of the earth to the surface of the earth, the relation between the value of ( g ) and distance ( (r) ) represented as a proportionality, is given by A ( cdot g propto frac{1}{r^{2}} ) В . ( g propto r ) c. ( g propto r^{2} ) D ( cdot g propto r^{o} ) | 11 |

513 | If the acceleration due to gravity at the surface of the earth is ( g ), the work done in slowly lifting a body of mass ( m ) from the earth’s surface to a height ( boldsymbol{R} ) equal to the radius of the earth is ( ^{mathrm{A}} cdot frac{m g R}{2} ) в. ( 2 m g R ) ( mathrm{c} cdot m g R ) D. ( _{m g} frac{R}{4} ) | 11 |

514 | The Sl unit of G is. A ( cdot N^{2} m^{2} / k g ) B. ( N m^{2} / k g ) c. ( N ) ml ( k g ) D. ( N m^{2} / k g^{2} ) | 11 |

515 | Gravitational force between two point masses ( m ) and ( M ) separated by a distance ( r ) is ( F ). now if a point mass ( 3 m ) is placed very next to ( mathrm{m} ), the total force on ( boldsymbol{M} ) will be A. ( F ) в. ( 2 F ) ( c .3 F ) D. ( 4 F ) | 11 |

516 | The diameters of two plantes are in the ration 4: 1 and their density in the ration 1: 2 The acceleration due to gravity on the planets will be in ratio, A ( cdot 1: 2 ) B. 2:3 ( c cdot 2: ) ( D cdot 4: ) | 11 |

517 | The scientist who gave me three laws of planetary motion was A. Newton B. Kepler c. Galileo D. Robert Boyle | 11 |

518 | A satellite close to the earth is in orbit above the equator with a period of revolution of 1.5 hours in the same sense as that of the earth. If it is above a point ( boldsymbol{P} ) on the equator at some time, it will be above ( P ) again after a time. A. 1.5 hours B. 1.6 hours if it is rotating from west to east c. ( frac{24}{27} ) hours if it is rotating from west to east D. none of these | 11 |

519 | A string tied on a roof can bear a maximum tension of 50kgwt. The minimum acceleration that can be acquired by a man of ( 98 k g ) to descend will be (Take ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} ) ) A ( cdot 9.8 m / s^{2} ) в. ( 4.9 m / s^{2} ) c. ( 4.8 m / s^{2} ) D. ( 5 m / s^{2} ) | 11 |

520 | Two bodies of masses ( 2 k g & 1.8 k g ) are separated by ( 20 m ) The force between them becomes 4 times at a distance of : A . ( 5 m ) B. ( 10 m ) ( c .20 m ) D. None of them | 11 |

521 | A man weight ( W ) on the surface of the earth and his weight at a height ( boldsymbol{R} ) from surface of the earth is ( (R ) is radius of the earth) A ( cdot frac{W}{4} ) в. ( frac{W}{2} ) c. ( W ) D. ( 4 W ) | 11 |

522 | If an orbiting satellite comes to a standstill suddenly, A. the satellite will move along the tangent. B. the satellite will move radically towards centre of the orbit C. the satellite will go to outer space and will be lost. D. the satellite will continue to move in the same orbit. | 9 |

523 | The gravitational potential difference between the surface of a planet and a point ( 20 m ) above it is ( 16 J / k g . ) Then the work done in moving a 2 kg mass by ( 8 m ) on a slope 60 degree from the horizontal, is: A . ( 11.1 mathrm{J} ) B. ( 5.5 J ) ( c .16 J ) D. 27.7 J | 11 |

524 | State whether the given statement is True or False: Acceleration due to gravity, ( boldsymbol{g}=frac{G M}{R^{2}} ) | 11 |

525 | A balloon filled with hydrogen gas is carried from earth to moon. Then the balloon will: A. neither fall nor rise B. fall with acceleration less than ( g ) c. fall with acceleration g D. rise with acceleration g | 11 |

526 | A man weighs ( 600 N ) on earth. What would be his approximate weight on moon? A . ( 100 N ) B. ( 200 N ) ( c .50 N ) D. ( 600 N ) | 9 |

527 | The escape velocity of a body depends upon its mass as ( mathbf{A} cdot m^{0} ) B . ( m^{text {। }} ) ( mathrm{c} cdot m^{3} ) D. ( m^{2} ) | 11 |

528 | The force acting on a mass of ( 1 g ) due to the gravitational pull on the earth is called 1 gw ( t . ) One ( g w t ) equals A. ( 1 N ) в. ( 9.8 N ) c. 980 dyne D. None of these | 11 |

529 | As a planet moves around the sun it sweeps equal areas in equal intervals of time. A. True B. False | 11 |

530 | Two identical spherical masses are kept at some distance. Potential energy when a mass ( m ) is taken from the surface of one sphere to the other A. increases continuously B. decreases continuously c. first increases, then decreases D. first decreases, then increases | 11 |

531 | A rain drop starts falling from a height of ( 2 k m . ) It falls with a continuously decreasing acceleration and attains its terminal velocity at a height of ( 1 k m . ) The ratio of the work done by the gravitational force in the first half to the that in the second half to the drops journey is A. 1: 1 and the time of fall of the drop in the two halves is ( a: 1 text { (where } a>1) ) B. 1: 1 and the time of fall of the drop in the two halves is ( a: 1 text { (where } a1 ) ) and the time of fall of the drop in the two halves is 1: 1 D. ( a: 1 ) (where ( a<1 ) ) and the time of fall of the drop in the two halves is 1: 1 | 11 |

532 | The evidence to show that there must be force acting on Earth and directed towards the Sun is. A. phenomenon of day and night B. apparent motion of the Sun around the Earth c. revolution of Earth around the sun D. deviation of the falling bodies towards east | 11 |

533 | The force of gravity cannot act at a distance. A . True B. False | 11 |

534 | State whether the given statement is True or False: The equation ( F=frac{G M_{1} M_{2}}{r^{2}} ) is valid for all bodies. A. True B. False | 11 |

535 | The height above the surface of earth at which acceleration due to gravity is half the acceleration due to gravity at surface of earth is ( left(R=6.4 times 10^{6} mright) ) A ( cdot 6.4 times 10^{6} m ) В. ( 2.6 times 10^{6} mathrm{m} ) c. ( 12.8 times 10^{6} m ) D. ( 19.2 times 10^{6} mathrm{m} ) | 11 |

536 | A small satellite revolves around a planet in an orbit just above planet’s surface. Taking the mean density of the planet ( 8000 mathrm{kg} m^{-3} ) and ( G=6.67 times ) ( 10^{-11} mathrm{N} m^{-2} / k g^{-2}, ) find the time period of the satellite. | 11 |

537 | At a given place where acceleration due to gravity is ( g m / s e c^{2}, ) a sphere of lead of density ( d k g / m^{3} ) is gently released in a column of liquid of density ( rho k g / m^{3} . ). ( boldsymbol{d}>boldsymbol{rho}, ) then immediately after the sphere is released inside the liquid, ¡t will: A . fall vertically with an acceleration of ( g ) m/ sec( ^{2} ) B. fall vertically with no acceleration c. fall vertically with an acceleration ( gleft(frac{d-rho}{d}right) ) D. fall vertically with an acceleration ( (g rho) / d ) | 11 |

538 | The value of acceleration due to gravity near the earth’s surface is A ( cdot 8.9 m / s^{2} ) в. ( 7.9 m / s^{2} ) ( mathrm{c} cdot 9.8 mathrm{m} / mathrm{s}^{2} ) D. ( 19.8 m / s^{2} ) | 11 |

539 | A straight tunnel is dug into the earth as shown in figure at a distance ( b ) from its center. A ball of mass ( m ) is dropped from one of its ends. Find the time it takes to reach the other end is approximately. | 11 |

540 | The value of acceleration due to gravity as we move from equator to pole A . increases B. decreases c. remains same D. becomes zero | 11 |

541 | The masses of sun and earth are ( M_{s} ) and ( M_{e}, ) respectively and the distance between them is ( R_{e s} ) then, the distance of a body of mass ( mathrm{m} ), from the earth along the line towards the sun, where the sun’s gravitational pull balances that of the earth is A ( cdot frac{R_{e s}}{sqrt{M_{s} / M_{e}}+1} ) В. ( frac{R_{e s}}{sqrt{M_{e} / M_{s}}+1} ) c. ( frac{R_{e s}}{sqrt{M_{s} / M_{e}}-1} ) D. ( frac{R_{e s}}{1-sqrt{M_{e} / M_{s}}} ) | 11 |

542 | Gravitational potential energy is A. the product of force and velocity B. the product of force and momentum C. the product of weight and height lifted by an object D. the product of force and displacement, if the particle is moving in a cirlce | 11 |

543 | In case of a planet revolving around the sun, the angle between the gravitational force and the radial vector is A. zero B. 90 c. 180 D. 45 | 11 |

544 | At what height above the earth’s surface, the value of ( g ) is same as that at a depth of ( 100 k m ? ) Hint: Take ( g_{h}=g_{d} ) | 11 |

545 | A small body starts falling onto the Sun from a distance equal to the radius of the Earth’s orbit. The initial velocity of the body is equal to zero in the heliocentric reference frame. Making use of Kepler’s laws, how long the body will be falling in days A . 64.5 B. 65 c. 60 D. None of these | 11 |

546 | When the radius of earth is reduced by ( 1 % ) with out changing the mass, then the acceleration due to gravity will A. increase by ( 2 % ) B. decrease by 1.5% C. increase by ( 1 % ) D. decrease by 1% | 11 |

547 | At a point very near earth’s surface, the acceleration due to gravity is g. What will be the acceleration due to gravity at the same point if the earth suddenly shrinks to half its radius without any change in its mass? ( A cdot 28 ) B. 48 c. ( g ) D. 3 | 11 |

548 | A feather of mass ( m ) and a hammer of mass ( 100 m ) are both released from rest from the same height on the surface of the moon. Mass of moon is ( M ) and radius of moon is ( R ). Both feather and hammer are released simultaneously. What is the acceleration of the hammer? A ( cdot frac{m v^{2}}{r} ) в. ( frac{G M}{R^{2}} ) c. ( frac{G M m}{R^{2}} ) D. ( _{100} frac{G M}{R^{2}} ) E ( cdot_{100} frac{G M m}{R^{2}} ) | 11 |

549 | An astronaut,inside an earth’s satellite experiences weightlessness because A. he is falling freely c. no reaction is exerted by the floor of the satellite D. he is far away from the earth’s surface | 11 |

550 | What is the range of gravitational force. ( ? ) ( A cdot 10^{-2} m ) B . ( 10^{-15} mathrm{m} ) c. infinite D. ( 10^{-10} mathrm{m} ) | 9 |

551 | The largest and the shortest distance of the earth from the sun is ( r_{1} ) and ( r_{2} ). Its distance from the sun when it is at perpendicular to the major axis of the orbit drawn from the sun: ( mathbf{A} cdotleft(r_{1}+r_{2}right) / 4 ) B . ( left(r_{1}+r_{2}right) /left(r_{1}-r_{2}right) ) ( mathbf{c} cdot 2 r_{1} r_{2} /left(r_{1}+r_{2}right) ) D. ( left(r_{1}+r_{2}right) / 3 ) | 11 |

552 | Time period depends on Gravitational constant (G),plank constant, (h) and speed of light (c), then ( mathrm{T} ) is proportional to ( ^{mathrm{A}} cdot frac{G^{1 / 2} h^{1 / 2}}{C^{3 / 2}} ) B. ( frac{G^{1 / 2} h}{C^{5 / 2}} ) ( ^{mathrm{C}} cdot frac{G h^{1 / 2}}{C^{5 / 2}} ) ( ^{mathrm{D} cdot frac{G^{1 / 2} h^{1 / 2}}{C^{5 / 2}}} ) | 11 |

553 | If a new planet is discovered rotating around sun with the orbital radius double that of the earth, then what will be its time period? (in earth’s days) A . 1032 B. 1023 ( c cdot 1024 ) D. 1043 | 11 |

554 | A body of mass ( m ) is taken from earth’s surface to q a height equal to radius of earth. the change in potential will be A . ( m g ) B. ( frac{1}{2} m g R ) c. ( 2 m g R ) D. ( frac{1}{4} m g R ) | 11 |

555 | A satellite is projected with a speed ( sqrt{frac{5}{6}} ) times of its escape speed from the earth’s surface. The initial speed of the satellite is parallel to the surface of the earth. The maximum distance of the satellite from the center of the earth will be A. ( 3 R ) в. ( 6 R ) ( c .5 R ) D. None of these | 11 |

556 | If two balls of some mass are dropped from the same height, would they fall down at the same time? | 11 |

557 | If the attractive force between two bodies of mass ( M_{1} ) and ( M_{2} ) and situated at a distance ( mathrm{R} ) is ( mathrm{F} ), then find the force ( F^{prime} ) between them at distance ( (R+d) ) in terms of ( F ) | 11 |

558 | The Sl unit of the universal gravitational constant ( G: ) ( mathbf{A} cdot N m K g^{-2} ) B. ( N m^{2} K g^{-2} ) c. ( N m^{2} K g^{-1} ) D. ( N m K g^{-1} ) | 11 |

559 | Two blocks, one of iron(i) and the other of wood(w) are dropped from a height at the same time. If the time taken by the blocks to reach the ground is ( T_{i} ) and ( T_{w} ) respectively, then find the relation between them? A ( . T_{i}T_{w} ) D. ( T_{i}=frac{1}{2 T_{w}} ) | 11 |

560 | The earth and the moon are attracted to each other by gravitational force.Does the earth attract the moon with a force the moon attracts the earth? Why? | 9 |

561 | Kepler’s first law provides information about A. areal velocity of a planet B. Shape of the orbit of the planettet c. Mass of the planet D. Distance of the planet from the sun | 11 |

562 | A small planet is revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force between the planet and the star were proportional to ( R^{-5 / 2}, ) then ( T ) would be proportional to A ( cdot R^{3 / 2} ) B. ( R^{3 / 5} ) c. ( R^{7 / 2} ) D. ( R^{7 / 4} ) | 11 |

563 | If the distance of earth from the sun reduces to one fourth of its present value then the length of the year will become A . ( 1 / 6 ) of present year B. 1/8 of present year c. ( 1 / 4 ) of present year D. ( 1 / 2 ) of present year | 11 |

564 | The weakest forces of interaction among all classified forces are A. electrostatic forces B. gravitational forces c. weak nuclear forces D. electromagnetic forces | 9 |

565 | If the change in the value of ( g ) at height ( h ) above earth surface is the same as that at depth ( xleft(x quad text { or } quad h<R_{e}right), ) then A ( cdot x=h^{2} ) в. ( x=h ) c. ( _{x}=frac{h}{2} ) D. ( x=2 h ) | 11 |

566 | Assume that life has existed on the surface of the moon, without changing its present acceleration due to gravity i.e., one sixth that on the surface of the moon. If 5 kg weight of sugar is purchased on the Earth and the Moon, how many cups of tea can be made out of it on the Earth and the Moon respectively? Note, From 100 g of sugar 10 cups of tea can be mode on the earth. ( left(g=10 mathrm{m} mathrm{s}^{-2}right) ) | 9 |

567 | The gravitational potential energy is the A. work done in bringing an object from infinity to radius ( r ) B. work done in moving an object around the earth C. work done by an object in attaining an object’s acceleration equal to ( 9.8 m / s^{2} ) D. work done in moving an object between two points horizontally | 11 |

568 | A person sitting in a chair in a satellite feels weightless because A. the earth does not attract the object in a satellite. B. the normal force by the chair on the parson balance the earht’s attraction. C. the normal force is zero. D. the person is satellite is not accelerated. | 11 |

569 | The mass of the moon is ( frac{1}{81} ) of the earth but the gravitational pull is ( frac{1}{6} ) of the earth. It is due to the fact that A the radius of earth is ( frac{9}{sqrt{6}} ) of the moon B. The radius of moon is ( frac{81}{6} ) of the eartt c. Moon is the satellite of the earth D. None of the above | 11 |

570 | Assertion If infinity is taken as reference, the gravitational potential is negative everywhere on the surface of earth. Reason Every body on its surface is bound to | 11 |

571 | At the centre of the earth, the value of ( g ) becomes A . zero B. unity c. infinity D. none of these | 11 |

572 | Where will it be profitable to purchase one kilogram sugar? A. At poles B. At equator C . At ( 45^{circ} ) latitude D. At ( 40^{circ} ) latitude | 11 |

573 | If the gravitational force of earth suddenly disappears, then which of the following is correct? A. weight of the body is zero B. mass of the body is zero c. both mass and weight become zero D. neither the weight nor the mass is zero | 11 |

574 | The value of acceleration due to gravity at height ( h ) from earth surface will become half its value on the surface if ( (R=text { radius of earth }) ) ( mathbf{A} cdot h=R ) в. ( h=2 R ) c. ( h=(sqrt{2}-1) R ) D. ( h=(sqrt{2}+1) R ) | 11 |

575 | A mass ( M ) is split into two parts ( m ) and ( (M-m), ) which are, then separated by a certain distance. The ratio ( boldsymbol{m} / boldsymbol{M} ) which maximizes the gravitational force between the parts is A . 1: 4 B. 1: 3 c. 1: 2 D. 1: 1 | 11 |

576 | Assertion A balloon filled with hydrogen will fall with acceleration ( frac{boldsymbol{g}}{boldsymbol{6}} ) on the moon. Reason Moon has no atmosphere. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 9 |

577 | A capillary tube is immersed vertically in water and the height of the water column is ( x ). When this arrangement is taken into a mine of depth ( d ), the height of the water column is ( y . ) If ( R ) is the radius of the earth, the ratio ( frac{x}{y} ) is : A ( cdotleft(1-frac{d}{R}right) ) B ( cdotleft(1-frac{2 d}{R}right) ) c. ( left(frac{R-d}{R+d}right) ) D. ( left(frac{R+d}{R-d}right) ) | 11 |

578 | How much faster than its normal rate should the earth rotate about its axis so that the weight of the body at the equator becomes zero? (Radius of the earth ( =6.4 times 10^{6} m ) and ( g=9.8 m / s^{2} ) A. Nearly 17 times B. Nearly 12 times c. Nearly 10 times D. Nearly 14 times | 11 |

579 | Consider the satellites revolving round the earth at different heights.The ratio of their orbital speed is 3: 2 . If one of them is at a height of ( 200 mathrm{Km} ), the height of the other satellite is (Radius of the earth is ( R=6400 mathrm{Km} ) A. ( 8450 K m ) в. 845 Кт c. ( 84.5 K m ) D. ( 84500 K m ) | 11 |

580 | A planet has twice the mass of earth and of identical size. What will be the height above the surface of the planet where its acceleration due to gravity reduces by ( 36 % ) of its value on its surface? | 11 |

581 | A satellite of mass ( 1000 k g ) is supposed to orbit the earth at a height of ( 2000 k m ) above the earth’s surface. Find its speed in the orbit. | 11 |

582 | The diameters of two planets are in ratio ( 4: 1 . ) Their mean densities have ratio ( 1: 2 . ) The ratio of ‘g’ on the planets will be: A .1: 2 B. 1: 4 c. 2: 1 D. 4: 1 | 11 |

583 | Two particles of masses ( 1.0 mathrm{kg} ) and ( 2.0 mathrm{kg} ) are placed at a separation of ( 50 mathrm{cm} . ) Assuming that the only forces acting on the particles are their mutual gravitation, find the initial accelerations of the two particles. | 11 |

584 | If the area swept by the line joining the sun and the earth from Feb 1 to Feb 7 is A, then the area swept by the radius vector from Feb 8 to Feb 28 is ( A cdot A ) B. 2A ( c cdot 3 A ) D. ( 4 A ) | 11 |

585 | Supposing the earth suddenly contracts to half of its radius, what will be the length of the day? A. 12 hours B. 8 hours c. 6 hours D. No change | 11 |

586 | The value of G does not depend on A. nature of the interacting bodies B. size of the interacting bodies c. mass of the interacting bodies D. all the above | 11 |

587 | A simple pendulum is taken to ( 64 K m ) above the earth’s surface. It’s time period will : A. increase by ( 1 % ) B. decrease by 1% c. increase by 2% D. decrease by 2% | 11 |

588 | If suddenly the gravitational force of attraction between earth and satellite revolving around it becomes zero, then the satellite will A. continue to move in its orbit with same velocity B. Move tangential to the original orbit with the same velocity c. Becomes sationary in its orbit D. Move towards the earth | 9 |

589 | Two point masses each equal to ( 1 k g ) attract one another with a force of ( 10^{-9} k g w t . ) Find the distance between the two point masses. Take: ( g= ) ( 9.8 m / s^{2} ) ( A cdot 8 c m ) B. ( 0.8 mathrm{cm} ) c. ( 80 mathrm{cm} ) D. ( 0.08 mathrm{cm} ) | 11 |

590 | Six particles each of mass ( m ) are placed at the corners of a regular hexagon of edge length ( a ). If a point mass ( m_{0} ) is placed at the centre of the hexagon, then the net gravitational force on the point mass ( boldsymbol{m}_{0} ) is : A ( cdot frac{6 G m^{2}}{a^{2}} ) в. ( frac{6 G m m_{0}}{a^{2}} ) c. zero D. none of these | 11 |

591 | The gravitational force is a A. contact force B. action at a distance force C. non contact force D. both (B) and (C) | 9 |

592 | Gravitational force between two bodies is 1 newton.If the distance between them twice, what will be the force? | 11 |

593 | is the force of attraction between any two bodies in the universe. A. Gravitation B. Polarityyy c. Induction D. Joule | 9 |

594 | If ( R=r ) adius of the earth and ( g= ) acceleration due to gravity on the surface of the earth, the acceleration due to gravity at a distance (r>R) from the centre of the earth is proportional to ( A ) в. ( r^{2} ) ( c cdot r^{-2} ) D. ( r^{-1} ) | 11 |

595 | Let ( V ) and ( E ) denote the gravitational potential and gravitational field at a point. It is possible to have A ( . V=0 ) and ( E=0 ) B. ( V=0 ) and ( E neq 0 ) c. ( V neq 0 ) and ( E=0 ) D. All of the above | 11 |

596 | Statement 1: Geostationary satellites may be setup in equatorial plane in orbits of any radius more than earth’s radius. Statement 2: Geostationary satellites have period of revolution of 24 hrs. | 11 |

597 | gravity ( g ) with distance ( d ) trom centre of the earth is best represented by ( (boldsymbol{R}= ) Earths radius): ( A ) ( B ) ( c ) ( D ) | 11 |

598 | If ( ^{prime} R^{prime} ) is the radius of the earth, then the height at which the weight of a body becomes ( frac{1}{4} ) of its weight on the surface of the earth is: A ( .2 . R ) в. ( R ) c. ( frac{3 R}{8} ) D. ( frac{R}{4} ) | 11 |

599 | Newton’s law of gravitation holds good for A. only small bodies B. only terrestrial bodies c. only big bodies D. all types of bodies | 11 |

600 | The acceleration due to gravity on the surface of a planet, whose mass and diameter are double that of the earth, is ( times 10^{-1} ) times the acceleration due to gravity on the surface of the earth. A. 5 B. 3 ( c cdot 0.5 ) D. 50 | 11 |

601 | If we assume only gravitational attraction between proton and electron in hydrogen atom and Bohr’s quantization rule to be followed, then the expression for the ground state energy of the atom will be the mass of proton is ( mathrm{M} ) and that of the electron is ( m): ) ( ^{mathrm{A}} cdot frac{G^{2} M^{2} m^{2}}{h^{2}} ) ( ^{text {В }} cdot frac{2 pi^{2} G^{2} M^{2} m^{3}}{h^{2}} ) c. ( frac{2 pi^{2} G M^{2} m^{3}}{h^{2}} ) D. None of these | 11 |

602 | A force which produces an acceleration in a body equal to acceleration due to gravity on earth, when the body has a unit mass is called A. Gravitational unit of force B. Gravity force ( c . ) Both D. None | 9 |

603 | The distance between two planets of masses ( mathrm{M} ) and ( 4 mathrm{M} ) is ‘a’ what is the gravitational potential at a point on a line joining them of which the gravitational intensity is zero? ( mathbf{A} cdot-frac{9 G M}{r} ) B. ( -frac{5 G M}{a} ) ( mathbf{c} cdot-frac{3 G M}{a} ) D. ( -frac{7 G M}{a} ) | 11 |

604 | The condition for a uniform spherical mass ( m ) of radius ( r ) to be a black hole is ( :[G=text { gravitational constant and } g= ) acceleration due to gravity]. ( ^{mathrm{A}}left(frac{2 G m}{r}right)^{1 / 2} leq c ) ( ^{mathrm{B}}left(frac{2 g m}{r}right)^{1 / 2}=c ) ( left(frac{2 G m}{r}right)^{1 / 2} geq c ) ( ^{mathrm{D}}left(frac{g m}{r}right)^{1 / 2} geq c ) | 11 |

605 | S.I. Unit of universal gravitational constant ( G ) is- ( ^{mathbf{A}} cdot frac{N m^{2}}{K g} ) в. ( frac{N m^{2}}{K g^{2}} ) c. ( frac{N m}{K g^{2}} ) D. ( frac{N m}{K g} ) | 11 |

606 | The rotation of the Earth having radius ( R ) about its axis speeds upto a value such that a man at latitude angle ( 60^{circ} ) feels weightless. The duration of the day in such case will be. A ( cdot 8 pi sqrt{frac{R}{g}} ) в. ( 8 pi sqrt{frac{g}{R}} ) ( ^{c} cdot pi sqrt{frac{R}{g}} ) D. ( 4 pi sqrt{frac{g}{R}} ) | 11 |

607 | A remote-sensing satellite of earth revolves in a circular orbit at a height of ( 0.25 times 10^{5} mathrm{m} ) above the surface of earth If earth’s radius is ( 6.38 times 10^{6} mathrm{m} ) and ( boldsymbol{g}=mathbf{9 . 8} quad boldsymbol{m} boldsymbol{s}^{-2}, ) then the orbital speed of the satellite is A ( .6 .67 mathrm{Kms}^{1} ) B. ( 7.92 mathrm{Kms}^{1} ) c. ( 8.56 mathrm{Kms}^{1} ) D. ( 9.13 mathrm{Kms}^{1} ) | 11 |

608 | Two satellites ( A ) and ( B ) go round the planet ( boldsymbol{P} ) in circular orbits having radii ( 4 R ) and ( R ) respectively. If the speed of the satellite ( A ) is ( 3 v, ) then the speed of satellite ( boldsymbol{B} ) will be A . ( 6 v ) в. ( 12 v ) c. ( frac{3 v}{2} ) D. ( frac{4 v}{3} ) | 11 |

609 | At what height in km over the earth’s pole the free fall acceleration decreases by one percent? (Assume the radius of the earth to be ( 6400 mathrm{km} ) ) A .32 B. 64 c. 80 D. 1.253 | 11 |

610 | In order to shift a body of mass ( mathrm{m} ) from a circular orbit of radius ( 3 R ) to a higher orbit of radius ( 5 R ) around the earth, the work done is? ( ^{A} cdot frac{3 G M m}{5 R} ) в. ( frac{G M m}{2 R} ) c. ( frac{2}{15} frac{G M m}{R} ) D. ( frac{G M m}{5 R} ) | 11 |

611 | At what depth (in terms of the radius of earth) the acceleration due to gravity will be ( frac{2 g}{5} ? ) | 11 |

612 | Mass of the earth is: A ( cdot frac{4}{3} pi R^{3}(A-B R) ) B ( cdot 4 pi R^{3}(A-B R) ) ( ^{mathbf{C}} cdot frac{4}{3} pi R^{3}left(A-frac{3}{4} B Rright) ) D ( cdot 4 pi R^{3}left(A-frac{3}{4} B Rright) ) | 11 |

613 | A stone is released from the top of a tower of height ( 19.6 mathrm{m} ). Calculate its final velocityjust before touching the ground. | 11 |

614 | Let ‘gh’ and ‘g ( _{d} ) ‘ be the acceleration due to gravity at height ‘h’ above the earth’s surface and at depth ‘ ( d ) below the earth’s surface respectively. IF ( boldsymbol{g}_{boldsymbol{h}}=boldsymbol{g}_{boldsymbol{d}} ) then the relation between ‘h’ and ‘ ( d ) is ( mathbf{A} cdot d=h ) B. ( d=frac{h}{2} ) ( c cdot d=frac{h}{4} ) D. ( d=2 h ) | 11 |

615 | A person on the surface of the moon: A. Does not feel the effect of earth’s gravity because the gravity due to moon is such stronger. B. Does not feel the effect of earth’s gravity. C. Does not feel the effect of earth’s gravity and moon gravity he is freely towards the earth. D. Feels only the combined effect of earth’s and moon gravity which are comparable in magnet | 9 |

616 | Two bodies, each of mass ( mathrm{M} ), are kept fixed with a separation 2 L. A particle of mass ( m ) is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are). A. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is ( 4 sqrt{frac{G M}{L}} ) B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is ( 2 sqrt{frac{G M}{L}} ) C. The minimum initial velocity of the mass ( m ) to escape the gravitational field of the two bodies is ( sqrt{frac{2 G M}{L}} ) D. The energy of the mass m remains constant | 11 |

617 | The unit of ( frac{G}{g} ) is: A. kg/m в. ( k g / m^{2} ) ( mathbf{c} cdot m^{2} / k g ) D. m/kg | 11 |

618 | Which of the following units can be used to express G? ( A cdot N K g^{-2} ) B. ( mathrm{Nm}^{-2} mathrm{Kg}^{2} ) ( mathrm{C} cdot mathrm{Nm}^{2} mathrm{Kg}^{-2} ) D. ( mathrm{Nm}^{-2} mathrm{Kg}^{-3} ) | 11 |

619 | If the earth shrinks to half of its radius without changing its mass, the duration of the day will be A. 48 hours B. 24 hours c. 12 hours D. 6 hours | 11 |

620 | A small body of super dense material, with mass equal to half of that of earth but whose size is very small compared to that of earth, starts from rest at the height h< ( A cdot sqrt{frac{2 h}{q}} ) в. ( sqrt{frac{4 h}{3 g}} ) c. ( sqrt{frac{2 h}{3 g}} ) D. ( sqrt{frac{h}{g}} ) | 11 |

621 | Which of the following statements regarding the gravitational attraction between man and the earth are correct? 1. The man and the earth pull each other with the same force 2. The earth pulls the man with more force than the man pulling the earth 3. The acceleration of the man due to the earth’s pull is more than that of the earth due to the man’s pull 4. The accelerations of the man and the earth are the same ( A cdot 2 ) and 3 B. 1 and 4 c. 1 and 3 D. 2 and 4 | 11 |

622 | If the acceleration due to gravity, ( g ), is ( 10 m / s^{2} ) at the surface of the earth (radius ( 6400 k m ) ), then at a height of 1600 km the value of ( g ) will be? ( operatorname{lin} m / s^{2} ) A . 4 B. 5 ( c .7 .5 ) D. 2.5 | 11 |

623 | The time period of a second’s pendulum inside a satellite will be A . zero B. ( 1 mathrm{sec} ) ( c cdot 2 sec ) D. infinite | 11 |

624 | No part of india is situated on the equator .Is it possible to have a geostationary satellite which always remains over New Delhi? | 11 |

625 | Assertion An astronaut experience weightlessness in a space satellite Reason When a body falls freely it does not experience gravity. | 11 |

626 | A satellite of mass ( m ) is orbiting around the earth at a height ( h ) above the surface of the earth. Mass of the earth is ( M ) and its radius is ( R ). The angular momentum of the satellite is independent of : A . в. ( M ) ( c cdot h ) D. None of these | 11 |

627 | An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel as shown in the figure. The water which comes out from the hole at the instant when hole is at height H above the ground, strikes the ground at a distance of ( x ) from P. | 11 |

628 | A mass ( mathrm{M} ) is lowered with the help of a string by a distancex at a constant acceleration ( frac{mathrm{g}}{2} . ) The magnitude of work doneby the string will be: ( ^{mathbf{A}} cdot frac{M g}{2} k ) B – ( frac{1}{2} M g x^{2} ) ( mathbf{c} cdot frac{1}{2} M g x ) D. ( M g x^{2} ) | 11 |

629 | An ice cube of size ( a=10 mathrm{cm} ) is floating in a tank (base ( =50 mathrm{cm} times ) 50cm ) partially filled with water. The change in gravitational potential energy, when ice completely melts is [Density of ice is ( 900 k g m^{-3} ) and ( g=10 m s^{-2} ) A. ( -0.0455 J ) в. ( -0.016 J ) c. ( -0.24 J ) D. ( -0.072 J ) | 11 |

630 | Suppose a new planet is discovered between Uranus and Neptune. Its time period would be A. less than that of Neptune. B. more than that of Neptune. c. equal to that of Neptune or Uranus. D. less than that of Uranus | 11 |

631 | The weight of an object at the centre of the earth of radius ( R ) is A. Zero B. Infinite C . ( R ) times the weight at the surface of the earth. D. ( 1 / R^{2} ) times the weight at surface of the earth. | 11 |

632 | The acceleration of free fall for object moving near the surface of Earth is: A ( cdot 9.81 m s^{-2} ) B. ( 9.31 m s^{-2} ) c. ( 8.81 m s^{-2} ) D. ( 10.81 m s^{-2} ) | 11 |

633 | Two block of mass ( m_{1} ) and ( m_{2} ) are kept a part d from each other. What happen to the magnitude of the force on ( m_{1} ) if the mass of ( m_{2} ) is doubled? A. It is quadrupled B. It is doubleo c. It remain the same D. It is halved E. It is quartered | 11 |

634 | Compare the acceleration due to gravity on the surface of a planet, whose mass and diameter are double that of the earth, with the acceleration due to gravity on the surface of the earth. A . 1: 2 B . 2: 1 c. 3: 4 D. 4: 1 | 11 |

635 | If we consider the gravitational force ( F ) between two objects of masses ( m_{1} ) and ( m_{2} ) respectively, separated by a distance ( R, ) and we double the distance between them, what is the new magnitude of the gravitational force between them? ( A cdot F / 4 ) B. F/2 ( c cdot F ) D. 2F E. 4 | 11 |

636 | Acceleration due to gravity of a body during free fall does not depend upon the: A. mass of earth B. mass of body c. universal gravitational constant D. radius of earth | 11 |

637 | Taking the gravitational potential at a point infinte distance away as zero, the gravitational potential at a point ( boldsymbol{A} ) is -5 unit. If the gravitational potential at a point infinite distance away is taken as +10 units, the potential at a point ( A ) is A. – 5 unit B . +5 unit c. +10 unit D. +15 unit | 11 |

638 | A planet is moving in an elliptical path around the sun as shown in figure.Speed of planet in position ( P ) and ( mathrm{Q} ) are ( boldsymbol{v}_{1} ) and ( boldsymbol{v}_{2} ) respectively with ( boldsymbol{S} boldsymbol{P}= ) ( r_{1} ) and ( S Q=r_{2} ) then ( v_{1} / v_{2} ) is equal to then A ( cdot frac{r_{1}}{r_{2}} ) в. ( frac{r_{2}}{r_{1}} ) c. consonant D. | 11 |

639 | A 10 kg satellite completes one revolution around the earth at a height of ( 100 mathrm{km} ) in 108 minutes. The work done by the gravitational force of earth will be? A . ( 108 times 100 times 10 ) J в. ( frac{108 times 10}{100} ) c. 0 J D. ( frac{100 times 10}{108} ) | 11 |

640 | Fill up the blank with suitable words. Value of universal gravitational constant ( G= ) | 11 |

641 | Q Type your question. orbiting some star. The planet is closer to the star as it moves from point 1 to point 2 than it is when it moves from point 3 to point 4 in its orbit. The dotted ine shows the orbital path. If the time it takes the planet to get from point 1 to point 2 is equal to the time it takes the planet to get from point 3 to point 4 then which of the following statements is true, according to Kepler’s laws of planetary motion? A. The average speed as the planet travels from 1 to 2 is the same as when it travels from 3 to 4 B. Area 1 in the diagram is equal to Area 2 C. Area 1 in the diagram is smaller than Area 2 D. The planet moves further from 3 to 4 from 1 to 2 E. The average speed as the planet moves from 3 to 4 is greater than when the planet moves from 1 to | 11 |

642 | Take the mean distance of the moon and the sun from the earth to be ( 0.4 times ) ( 10^{6} k m ) and ( 150 times 10^{6} k m ) respectively. Their masses are ( 8 times 10^{22} k g ) and ( 2 times ) ( 10^{30} k g ) respectively. The radius of the earth is ( 6400 mathrm{km} ). Let ( Delta F_{1} ) be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ( Delta F_{2} ) be the difference in the force exerted by the sun at the nearest and farthest points o the earth. Then, the number closest to ( frac{Delta F_{1}}{Delta F_{2}} ) is : A .2 B. ( 10^{-2} ) ( c .0 .6 ) D. | 11 |

643 | ENERGY OF AN ORBITING SATELLITE A comet orbits the sun in a highly elliptical orbit. Which of the following quantities remains constant throughout its orbit? (i) Linear speed (ii) Angular speed (iii) Angular momentum (iv) Kinetic energy (v) Potential energy (vi)Total energy ( A cdot(i),(text { ii) },( text { iii) } ) B. (iii), (iv), (v) c. (iii) and (vi) D. (ii), (iii) and (vi) | 11 |

644 | A high jumper can jump ( 2.0 mathrm{m} ) on earth, With the same effort how high will he be able to jump on a planet whose density is one-third and radius one-fourth those of the earth? ( A cdot 4 m ) B. 8 m ( c cdot 18 m ) D. 24 m | 11 |

645 | If the acceleration due to gravity g at the earth’s surface is ( 9.8 m s^{-2} ) and mass of the earth is 80 times that of moon, radius of earth 4 times that of the moon, the value of ( g ) at the moon’s surface will be approximately equal to? ( mathbf{A} cdot 4 m s^{-2} ) В. ( 1.96 m s^{-2} ) ( mathrm{c} cdot 27 mathrm{ms}^{-2} ) D. ( 16 m s^{-2} ) | 11 |

646 | A remote – sensing satellite of earth revolves in a circular orbit at a height of ( 0.25 times 10^{6} mathrm{m} ) above the surface of earth If earth’s radius is ( 6.38 times 10^{6} m ) and ( g=9.8 m s^{-2}, ) then the orbital speed of the satellite is: ( mathbf{A} cdot 6.67 k m s^{-1} ) B . ( 7.76 mathrm{km} mathrm{s}^{-1} ) c. ( 8.56 k m s^{-1} ) D. ( 9.13 mathrm{km} mathrm{s}^{-1} ) | 11 |

647 | An artificial satellite moving in a circular orbit around the earth has a total (kinetic ( + ) potential ) energy ( frac{boldsymbol{E}_{0}}{boldsymbol{4}} ) Its potential energy is A ( cdot frac{E_{0}}{4} ) в. ( frac{E_{0}}{2} ) c. ( frac{E_{0}}{8} ) D. ( E_{0} ) | 11 |

648 | Two spherical bodies of mass ( mathrm{M} ) and ( 5 mathrm{M} ) and radii R and ( 2 mathrm{R} ) respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only. then the distance covered by the smaller body just before collision is A . 1.5 R в. 2.5 c. 4.5 R D. 7.5R | 11 |

649 | The height at which the acceleration due to gravity becomes ( g / 9 ) (where ( g= ) the acceleration due to gravity on the surface of the earth) in terms of ( R ), the radius of the earth, is A. ( R / 2 ) в. ( sqrt{2} R ) ( c .2 R ) D. ( frac{R}{sqrt{2}} ) | 11 |

650 | For a satellite to be geostationary, which of the following are essential conditions? This question has multiple correct options A. It mu always be stationed above the equator. B. It must rotate from west to east c. It must be about ( 36,000 mathrm{km} ) above the earth. D. Its orbit must be circular, and not elliptical | 11 |

651 | Two projectiles, one fired from the surface of the earth with speed ( 5 m / s ) and the other fired from the surface of a planet with initial speed ( 3 m / s, ) trace identical trajectories. Neglecting friction effect the value of acceleration due to gravity on the planet is: A. ( 5.9 mathrm{m} / mathrm{s}^{2} ) в. ( 3.5 mathrm{m} / mathrm{s}^{2} ) ( mathbf{c} cdot 16.3 mathrm{m} / mathrm{s}^{2} ) D. ( 8.5 mathrm{m} / mathrm{s}^{2} ) | 11 |

652 | Assume that the earth moves around the sun in a circular orbit of radius ( mathrm{R} ) and there exists a planet which also moves around the sun in circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is A ( cdot frac{-2}{3} R ) B. ( frac{2}{3} R ) c. ( frac{-1}{3} R ) D. ( frac{R}{sqrt{2}} ) | 11 |

653 | A mass ( M ) is split into two parts ( m ) and ( (M-m), ) which are then separated by a certain distance. What ratio ( (boldsymbol{m} / boldsymbol{M}) ) maximizes the gravitational force between the parts. | 11 |

654 | The distance between earth and moon is about ( 3.8 times 10^{5} mathrm{km} . ) At what points will the net gravitational force of earthmoon system be zero? [Given the mass of the earth is 81 times the moon’s mass]. (Hint: Assume a body of unit mass at the null point) | 11 |

655 | Assertion It takes more fuel for a spacecraft to travel from the earth to the Moon than for the return trip. Reason The point of zero gravitational field intensity due to the earth and the Moon is Iying nearer to the Moon, i.e., in the diagram shown, for ( r ) ( r_{0}, E_{g} ) is towards the Moon’s centre, and ( operatorname{at} r=r_{0}, E_{g} ) is zero. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect and Reason is correct | 11 |

656 | A ball of mass ( m ) is fired vertically upwards from the surface of the earth with velocity ( n nu_{e}, ) where ( nu_{e} ) is the escape velocity and ( n>1 . ) To what height will the ball rise? Neglecting air resistance, take radius of the earth as ( boldsymbol{R} ) A ( cdot frac{R}{n^{2}} ) в. ( frac{R}{left(1-n^{2}right)} ) c. ( frac{R n^{2}}{left(1-n^{2}right)} ) D. ( R n^{2} ) | 11 |

657 | Consider two satellites ( A ) and ( B ) of equal mass ( mathrm{m}, ) moving in the same circular orbit about the earth, but in the opposite sense as shown in Figure. The orbital radius is ( r ). The satellites undergo a collision which is perfectly inelastic. For this situation, mark out the correct statement(s). [Take mass of earth as ( mathrm{M}] ) (6) A. The satellites starts falling towards center of the earth. B. The total energy of the two satellites plus earth system just after collision is ( -2(G M m) / r ) C. The total energy of two satellites plus earth system just after collision is ( -(G M m) / 2 r ) D. The combined mass(two satellites) will fall towards the earth just after collision. | 11 |

658 | A particle falling under gravity describes ( 80 f t ) in a certain sec. How long does it take to describe next ( 112 f t ) ( ?left[boldsymbol{g}=boldsymbol{3} 2 boldsymbol{f} boldsymbol{t} boldsymbol{s}^{-2}right] ) ( mathbf{A} cdot 1 s ) B . ( 2 s ) c. ( 3 s ) D. ( 4 s ) | 11 |

659 | Assertion The smaller the orbit of a planet around the Sun, the shorter is the time it takes to complete. Reason According to Kepler’s third law of planetary motion, square of time period is proportional to cube of mean distance from Sun. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect and Reason is correct | 11 |

660 | Three particles of identical masses ( boldsymbol{m} ) are kept at the vertices of an equilateral triangle of each side length ‘a’. Find the gravitational force of attraction on any one of the particles. | 11 |

661 | The maximum vertical distance through which a full dressed astronaut canjump on the earth is ( 0.5 mathrm{m} ) Estimate the maximum vertical distance through which he can jump on the moon, which has a mean density ( 2 / 3 ) rd that of the earth and radius one quarter that of the earth. A . ( 1.5 mathrm{m} ) B. 3 m ( c cdot 6 m ) D. 7.5 ( m ) | 9 |

662 | Near the earth’s surface time period of a satellite is 1.4 hrs. Find its time period if it is at the distance ( ^{prime} 4 R^{prime} ) from the centre of the earth. A . 32 hrs B. ( left(frac{1}{8 sqrt{2}}right) ) hrs c. ( 8 sqrt{2} hbar r s ) D. 16 hrs | 11 |

663 | The radius in kilometers to which the present radius of the earth ( (boldsymbol{R}= ) ( 6400 k m) ) is to be compressed so that the escape velocity is increased to 10 times is : A. 6.4 B. 64 ( c cdot 640 ) D. 4800 | 11 |

664 | A ball of mass ( mathrm{m} ) is thrown vertically upward from the ground and reaches a height h before momentarily coming to rest.If ( g ) is acceleration due to gravity,the impulse received by the ball due to gravity force during its flight is ( mathbf{A} cdot sqrt{2 m^{2} g h} ) в. ( sqrt{4 m^{2} g h} ) ( mathbf{c} cdot sqrt{8 m^{2} g h} ) D. ( 4 sqrt{m^{2} g h} ) | 11 |

665 | The value of ( ^{prime} g^{prime} ) will be ( 1 % ) of its value at the surface of the earth at a height of ( left(R_{e}=6400 k mright) ) ( A cdot 6400 mathrm{km} ) B. 57600 km c. ( 12560 mathrm{km} ) D. 64000 km | 11 |

666 | A planet is moving around the Sun in a circular orbit of circumference ( C . ) The work done on the planet by the gravitational force ( F ) of the Sun is ( k F C ) then the value of ( k ) is | 11 |

667 | Two bodies of masses ( m_{1} ) and ( m_{2} ) are placed at distance X from each other. IfX is kept constant and the masses of the two bodies are increased to ( 2 m_{1} ) and ( 2 m_{2}, ) then the value of gravitational force between them will become A. 4 times B. 2 times c. 8 times D. ( 1 / 4 ) times | 11 |

668 | A mass ( mathrm{m} ) is suspended form a sensitive spring balance kept in a satellite. The reading of the balance is ( W_{1} ) when the satellite is in an orbit of radius ( mathrm{R} ) and is ( W_{2} ) when it is in an orbit of radius ( 2 mathrm{R} ). Then A. ( W_{1}>W_{2} ) в. ( W_{1}<W_{2} ) c. ( W_{1}=W_{2} ) D. cannot be predicted | 11 |

669 | Two spherical lumps of clay attract each other with some amount of gravitational force, as explained by Newton’s law of universal gravitation. If add clay to one lump and to the other so that the mass of one is 5 times as much as before and the mass of the other is 3 times as much as before, and I move the lumps (still spherical) so that their centers are now 4 times as far apart as before, how does the new gravitational force between them compare? A. The new force is slightly smaller. B. The new force is slightly greater. c. The new force is more than 3 times as great D. The new force is less than one-third as greatt E. We cannot answer this question without knowing the universal gravitational constant | 11 |

670 | Assertion In a free fall, weight of a body becomes effectively zero. Reason Acceleration due to gravity acting on a body having free fall is zero. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

671 | A body weighs ( 160 mathrm{N} ) on the earth. Find its weight on the other planet whose: (a) mass is ( frac{1}{4} ) times the mass of earth and radius ( frac{1}{3} ) times that of the earth. (b) mass is ( frac{5}{2} ) times the mass of earth and radius ( frac{4}{5} ) times that of the earth. | 11 |

672 | A moon of Saturn has a nearly circular orbit of radius ( R ) and an orbit period of ( T ). Which of the following expressions gives the mass of Saturn? ( ^{A} cdot frac{2 pi R}{T} ) в. ( frac{4 pi^{2} R}{T} ) ( ^{mathbf{c}} cdot frac{2 pi R^{3}}{left(G T^{2}right)} ) D. ( frac{4 pi^{2} R^{2}}{left(G T^{2}right)} ) E ( cdot frac{4 pi^{2} R^{3}}{left(G T^{2}right)} ) | 11 |

673 | Gravity is what makes objects orbit around other objects, and gravity is a reflection of an object’s mass. So why doesn’ the mass of the objects appear in Kepler’s third law?? | 11 |

674 | Two spherical bodies the mass ( M ) and ( mathbf{5} M boldsymbol{m} ) and radii ( boldsymbol{R} ) and ( mathbf{2} boldsymbol{R} ) respectively are released in free space with initial separation between their centres equal to ( 12 R ) If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is: ( mathbf{A} cdot 2.5 R ) B. ( 4.5 R ) c. ( 7.5 R ) D. ( 1.5 R ) | 11 |

675 | A satellite moves in a circular orbit around the earth at height ( boldsymbol{R} / 2 ) from earth’s surface where ( R_{e} ) is the radius of the earth. Calculate its period of revolution. Given ( boldsymbol{R}_{e}=mathbf{6 . 3 8} times mathbf{1 0}^{mathbf{6}} mathbf{m} ) | 11 |

676 | A planet revolves about the sun in elliptical orbit. The arial velocity ( left(frac{boldsymbol{d} boldsymbol{A}}{boldsymbol{d} boldsymbol{t}}right) ) of the planet is ( 4.0 times 10^{16} m^{2} / s . ) The least distance between planet and the sun is ( 2 times 10^{12} mathrm{m} . ) Then the maximum speed of the planet in ( mathrm{km} / mathrm{s} ) is ( A cdot 10 ) B. 20 ( c cdot 40 ) D. none of these | 11 |

677 | Two particles of masses ( 4 k g ) and ( 6 k g ) are at rest separated by 20 m. If they move towards each other under mutual force of attraction, the position of the point where they meet is ( mathbf{A} cdot 12 m ) from ( 4 k g ) body B. ( 12 mathrm{m} ) from ( 6 mathrm{kg} ) body c. ( 8 m ) from 4 kg body D. ( 10 m ) from ( 4 k g ) body | 11 |

678 | An artificial satellite moves in a circular orbit around the earth. Total energy of the satellite is given by ( boldsymbol{E} ). The potential energy of the satellite is: A . ( -2 E ) в. ( 2 E ) c. ( frac{2 E}{3} ) D. ( -frac{2 E}{3} ) | 11 |

679 | The horizontal component of the weight of a body of mass ( m ) is A . ( m g ) B. ( frac{mathrm{mg}}{2} ) c. 0 D. Infinity | 9 |

680 | Escape velocity from earth is 11.2km/sec. Another planet of same mass has radius ( frac{1}{4} ) times that of earth. What is the escape velocity from this planet? A. ( 11.2 k m / )sec в. ( 44.8 k m / )sec c. ( 22.4 k m / )sec D. ( 5.6 k m / )sec | 11 |

681 | A satellite moves around the earth in a circular orbit with speed ( V ). If ( m ) is mass of the satellite then its total energy is A ( cdot frac{1}{2} m V^{2} ) в. ( m V^{2} ) c. ( -frac{1}{2} m V^{2} ) D. ( frac{3}{2} m V^{2} ) | 11 |

682 | Two particles of equal mass go around a circle of radius ( R ) under the action of their mutual gravitational attraction.The speed of each particle is ( ^{mathbf{A}} cdot_{v}=frac{1}{2 R} sqrt{left(frac{1}{G m}right)} ) в. ( v=sqrt{left(frac{G m}{2 R}right)} ) ( ^{mathrm{c}} v=sqrt{left(frac{G m}{R}right)} ) D. ( v=sqrt{left(frac{4 G m}{R}right)} ) | 11 |

683 | The ratio of mean distances of three planets from the sun are ( 0.5,1,1.5, ) then the square of time periods are in the ratio of: A. 1: 4: 9 B. 1: 9: 4 c. 1: 8: 27 D. 2: 1: 3 | 11 |

684 | What will be change in value of gravitational acceleration with increase in ( r ) from the center of the earth? A. Decreases continuously B. Increases continuously C. Initially increases then decreases D. Initially decreases then increases | 11 |

685 | A particle is dropped on Earth from height ( mathbf{R}(text { radius of Earth }) ) and it bounces back to a height ( mathbf{R} / mathbf{2} ) coefficient of restitution for collision is (ignore air resistance and rotation of Earth) ( A cdot frac{2}{3} ) B. ( sqrt{frac{2}{3}} ) ( c cdot sqrt{frac{1}{3}} ) D. ( sqrt{frac{1}{2}} ) | 9 |

686 | The radius of the nearly circular orbit of mercury is ( 5.8 times 10^{10} m ) and its orbital period is 88 days. If a hypothetical planet has an orbital period of 55 days, what is the radius of its circular orbit? | 11 |

687 | Sl unit of ( G ) is ( N m^{2} k g^{-2} ) Which of the following can also be used as the Sl unit of G? A ( cdot m^{3} k g^{-1} s^{-2} ) B . ( m^{2} k g^{-2} s^{-1} ) c. ( m k g^{-1} s^{-1} ) D. ( m^{3} k g^{-3} s^{-2} ) | 11 |

688 | Suppose(God forbid) due to some reason, the earth expands to make its volume eight-fold. What you expect your weight to be? A. Two-fold B. One-half c. one-fourth D. Unaffected | 11 |

689 | A spaceship is released in a circular orbit near the Earth’s surface. How much additional velocity will have to be given to the spaceship in order to escape out of this orbit? ( begin{array}{ll}text { A. } 3.28 & text { m/s }end{array} ) В. ( 3.28 times 10^{3} mathrm{m} / mathrm{s} ) C ( .3 .28 times 10^{7} mathrm{m} / mathrm{s} ) D. ( 3.28 times 10^{-3} mathrm{m} / mathrm{s} ) | 11 |

690 | If the radius of a planet is doubled keeping density constant, what will be the value of escape velocity A. Escape velocity remains same B. Escape velocity doubles c. Escape velocity becomes halved D. Escape velocity becomes one fourth | 11 |

691 | Assuming the earth to be a uniform sphere of radius ( 6400 mathrm{km} ) and density ( 5.5 mathrm{g} / mathrm{c} . mathrm{c}, ) find the value of ( mathrm{g} ) on its surface. ( G=6.66 times 10^{-11} N m^{2} k g^{-2} ) ( mathbf{A} cdot=3.82 m s^{-2} ) В. ( =9.82 m s^{-2} ) ( mathbf{c} .=19.82 m s^{-2} ) ( mathrm{D} cdot=2 m s^{-2} ) | 11 |

692 | Assertion When the distance between two bodies is doubled and also the mass of each body is doubled, the gravitational force between them remains the same Reason According to Newton’s law of gravitation, force is directly proportional to mass of the bodies and inversely proportional to square of the distance between them A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

693 | One kilogramme force is the force due to gravity on a mass of A . ( 1 g ) B. ( 10 g ) ( c .100 g ) D. ( 1000 g ) | 9 |

694 | Suppose, the acceleration due ot gravity at the earth’s surface is ( 10 m s^{-2} ) and at the surface of Mars it is ( 4.0 m s^{-2} . A 60 ) kg passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure bests represents the weight (net gravitational force) of the passenger as a function of time? ( mathbf{A} cdot A ) B. ( B ) ( c cdot C ) ( D . D ) | 11 |

695 | Why will a sheet of paper fall slower than one that is crumpled into a ball? | 11 |

696 | A body weight ( 72 N ) on the surface of the earth. What is the gravitational force acting on it due to the earth at a height equal to half the radius of the earth from the surface? A. ( 16 N ) в. 32 N c. ( 8 N ) D. ( 48 N ) | 11 |

697 | Assertion The value of acceleration due to gravity does not depend upon mass of the body Reason Acceleration due to gravity is a constant quantity A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

698 | If you have to purchase 100 kg weight of gold, which place would you prefer-the Earth or the Moon? Similarly, if you have to sell gold, which place you prefer – The earth or the moon? Explain. | 9 |

699 | The acceleration due to gravity ( g ) and mean density of earth ( rho ) are related by which of the following relations? ( [G= ) gravitational constant and ( mathrm{R}= ) radius of earth]. A ( cdot rho=frac{4 pi g R^{2}}{3 G} ) В ( cdot rho=frac{4 pi g R^{3}}{3 G} ) ( mathbf{c} cdot rho=frac{3 G}{4 pi g R} ) D. ( rho=frac{3 G}{4 pi g R^{3}} ) | 11 |

700 | Imagine a planet having the same density as that of the earth but radius is three times the radius of the earth. If acceleration due to gravity on the surface of the earth is ( g ) and that on the said planet is ( g^{prime} ), then A ( cdot g^{prime}=frac{g}{9} ) B . ( g^{prime}=9 g ) c. ( g^{prime}=frac{g}{27} ) D. ( g^{prime}=3 g ) | 11 |

701 | The height from earth’s surface at which acceleration due to gravity becomes ( frac{g}{4} ) is (where ( g ) is acceleration due to gravity on the surface of earth and ( R ) is radius of earth) A ( cdot sqrt{2} R ) в. ( R ) c. ( frac{R}{sqrt{2}} ) D. 2R | 11 |

702 | Nikhil calculates the change in gravitational potential energy at a height of ( 5 mathrm{km} ) from the surface of earth using the equation ( U=-G M m / r ) and Varun calculates this energy using the formula ( U= ) mgh. The energies calculated have different numerical values. A . True B. False | 11 |

703 | If density of earth increases 4 times and its radius becomes half of what it is, our weight will: A. be 4 times its present value B. be doubled c. remain same D. be halved | 11 |

704 | The height at which the acceleration due to gravity becomes ( frac{mathbf{g}}{mathbf{g}} ) (where ( mathbf{g}= ) the acceleration due to gravity on the surface of the earth) in terms of ( mathbf{R} ), the radius of the earth, is: A . 2 R B. ( frac{mathrm{R}}{sqrt{2}} ) c. ( mathrm{R} / 2 ) D. ( sqrt{2} mathrm{R} ) | 11 |

705 | The weight of a boy on the surface of moon is ( 300 N . ) The weight of this boy on the surface of earth is: ( mathbf{A} cdot 300 N ) в. ( 5 N ) ( c .50 N ) D. ( 1800 N ) | 9 |

706 | Value of g is: A. maximum at poles B. maximum at equator C . same everywhere D. minimum at poles | 11 |

707 | Two solid spheres of same size of a certain metal are placed in contact with each other. Prove that the gravitiational force acting between them is directly proportional to the fourth power of their radius. | 11 |

708 | Rain drops are falling with a constant speed by the time they reach the ground because. A. Rain drops originate in outer space where the gravitational forces are negligible B. The force due to air resistance increases with the speed of the rain drops until it balances the gravitational force C. Rain drops are two light and hence not affected by acceleration due to gravity D. The force due to air resistance is constant and balances the gravitational force | 11 |

709 | ACCELERATION DUE TO GRAVITY OF THE EARTH Radius of earth is ( 6400 mathrm{km} ) and that of | 11 |

710 | A planet of mass ( 3 times 10^{29} mathrm{gm} ) moves around a star with a constant speed of ( 2 times 10^{8} m s^{-1} ) in a circle of radii ( 1.5 times ) ( 10^{12} mathrm{m} . ) The gravitational force exerted on the planet by the star is A ( .6 .67 times 10^{22} ) dyne B . ( 6.67 times 10^{26} ) N c. ( 8 times 10^{26} mathrm{N} ) D. ( 8 times 10^{27} ) dyne | 11 |

711 | What is gravitational potential energy? Explain with the help of an example. | 11 |

712 | A particle when thrown. moves such that it passes from same height at 2 and ( 10 s, ) the height is: ( mathbf{A} cdot g ) в. ( 2 g ) c. ( 5 g ) D. ( 10 g ) | 11 |

713 | The escape velocity on a planet is ( boldsymbol{v} . ) If the radius of the planet contracts to ( frac{1}{4} ) of present value without any change in its mass, the escape velocity will be A. halved B. doubled c. quadrupoled D. becomes one fourth | 11 |

714 | The escape velocity from the earth is 11 ( mathrm{km} s^{-1} . ) The escape velocity from a planet having twice the mass and twice the radius will be : A . ( (11 times sqrt{12}) k m s^{-1} ) B. ( 11 k m s^{-1} ) c. ( frac{11}{2} k m s^{-1} ) D. ( (11 times sqrt{2}) k m s^{-1} ) | 11 |

715 | At a place, the value of ‘g’ is less by ( 1 % ) than its value on the surface of the Earth (Radius of Earth, ( boldsymbol{R}=mathbf{6 4 0 0 k m} ) ). The place is: A. ( 64 mathrm{km} ) below the surface of the earth B. ( 64 mathrm{km} ) above the surface of the earth c. ( 30 mathrm{km} ) above the surface of the earth D. 32 km below the surface of the earth | 11 |

716 | A mass of ( M ) at rest is broken into two pieces having masses ( m ) and ( (M-m) ) The two masses are then separated by a distance. The gravitational force between them will be the maximum when the ratio of the masses ( [m: ) ( (M-m)] ) of the two parts is: A . 1: 1 B. 1: 2 ( c cdot 1: 3 ) D. 1: 4 | 11 |

717 | Find out the correct relation for the dependance of change in acceleration due to gravity on the angle at the latitude due to rotation of earth? A ( . d g propto cos phi ) B. ( d g propto cos ^{2} phi ) c. ( d g propto cos ^{3 / 2} phi ) D. ( d g propto frac{1}{cos phi} ) | 11 |

718 | A remote sensing satellite is revolving in an orbit of radius x over the equator of earth. If the area on each surface in which satellite can not send message is ( operatorname{given} operatorname{as}left(1-frac{sqrt{x^{2}-R^{2}}}{x}right) s pi R^{2} . ) Find ( s ) | 11 |

719 | The masses and radii of the earth and the Moon are ( M_{1}, R_{1} ) and ( M_{2}, R_{2} ) respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is? A ( cdot sqrt{frac{2 Gleft(M_{1}+M_{2}right)}{d}} ) B. ( sqrt{frac{4 Gleft(M_{1}+M_{2}right)}{d}} ) c. ( sqrt{frac{4 G M_{1} M_{2}}{d}} ) D. ( sqrt{frac{Gleft(M_{1}+M_{2}right)}{d}} ) | 11 |

720 | A ball is dropped from a satellite revolving around the earth at height of 120km. The ball will A. Continue to move with same speed along a straight line tangentially to the satellite at that time B. Continue to move with same speed along the original orbit of satellite c. Fall down to earth gradually D. Go far away in space | 11 |

721 | whose hemispherical base is of diameter ( 0.20 mathrm{m} . ) The height of the flask is ( 0.25 mathrm{m} ). The flask is filled to the brim with 2.5 litres ( left(1 text { litre }=10^{-3} m^{3}right) ) of water and sealed with a glass lid. What is the approximate magnitude of the total vertical force exerted by the water on the curved surface of the flask? (Take the acceleration due to gravity, ( g, ) to be ( 10 m s^{-2} ) ). ( A cdot O N ) B. 78.5 c. 53.5 N D. 25.0 | 11 |

722 | The gravitational force between two objects in ( 200 N ) How should the distance between these objects be changed so that force between them becomes ( 50 N ? ) | 11 |

723 | For the moon to cease to remain the earth’s satellite its orbital velocity has to increase by a factor of ( A cdot 2 ) B. ( sqrt{2} ) ( c cdot 1 sqrt{2} ) D. ( sqrt{3} ) | 11 |

724 | How the value of ( g ) varies with height. | 11 |

725 | Variation in the Acceleration Due to Gravity: Inside the earth: ( g=g_{0} frac{x}{R_{0}}(x ) is distance from the centre of the earth). | 11 |

726 | The attached figure shows a planet revolving a star. It was recorded that the planet takes 50 days to travel from ( T ) to U. Which other two observations could be 50 days apart? A. ( mathrm{V} ) and ( mathrm{W} ) B. Wand Y c. ( x ) and ( Y ) D. ( x ) and ( z ) E. ( Y ) and | 11 |

727 | Three planets of same density and with radii ( mathbf{R}_{1}, mathbf{R}_{2} ) and ( mathbf{R}_{3}, ) such that ( mathbf{R}_{1}= ) ( 2 mathrm{R}_{2}=3 mathrm{R}_{3}, ) have gravitation fields on the surfaces ( mathrm{E}_{1}, mathrm{E}_{2}, mathrm{E}_{3} ) and escape velocities ( mathbf{v}_{mathbf{1}}, mathbf{v}_{mathbf{2}}, mathbf{v}_{mathbf{3}} ) respectively, Then This question has multiple correct options A ( cdot frac{mathrm{E}_{1}}{mathrm{E}_{2}}=frac{1}{2} ) в. ( frac{mathrm{E}_{1}}{mathrm{E}_{3}}=3 ) c. ( frac{v_{1}}{v_{2}}=2 ) D. ( frac{v_{1}}{v_{3}}=frac{1}{3} ) | 11 |

728 | An astronaut whose mass is ( 84 k g ) on earth will have a mass of approximately 14 ( k g ) on the moon A. True B. False | 9 |

729 | Escape velocity for a projectile at earth’s surface is ( v_{e} . ) A body is projected form earth’s surface with velocity ( 2_{v_{e}} ) The velocity of the body when it is at infinite distance from the centre of the earth is A ( cdot v_{e} ) B. ( 2 v_{e} ) ( c cdot sqrt{2 v} ) D. ( sqrt{3} v_{e} ) | 11 |

730 | If ( F ) is the force between two bodies of masses ( m_{1} ) and ( m_{2} ) at certain separation. Find the force between ( sqrt{2} m_{1} ) and ( sqrt{3} m_{2} ) at same separation. | 11 |

731 | The orbital radius of moon around the earth is ( 3.8 times 10^{8} ) meter and its time period is 27.3 days. The centripetal acceleration of moon will be A. ( -2.4 times 10^{-3} mathrm{m} / mathrm{s}^{2} ) B. ( 11.2 m / s^{2} ) c. ( 2.7 times 10^{-3} mathrm{m} / mathrm{s}^{2} ) D. ( 9.8 m / s^{2} ) | 11 |

732 | Average distance of the earth from the sun is ( L_{1} . ) If one year of the earth ( =D ) days, one year of another planet whose average distance from the sun is ( L_{2} ) will be ( ^{mathrm{A}} cdot_{D}left(frac{L_{2}}{L_{1}}right)^{1 / 2} ) days B. ( quad Dleft(frac{L_{2}}{L_{1}}right)^{3 / 2} ) days ( ^{mathbf{C}} cdot_{D}left(frac{L_{2}}{L_{1}}right)^{2 / 3} ) days D. ( Dleft(frac{L_{L}}{L_{1}}right) ) days | 11 |

733 | A body suspended from a spring balance is placed in a satellite. Reading in balance is ( W_{1} ) when the satellite moves in an orbit of radius ( R ). Reading in balance is ( W_{2} ) when the satellite moves in an or bit of radius ( 2 R ). Then. A. ( W_{1}=W_{2} ) в. ( W_{1}>W_{2} ) ( mathbf{c} cdot W_{1}<W_{2} ) D. ( W_{1}=2 W_{2} ) | 11 |

734 | What is meant by torque due to gravity? | 11 |

735 | The time period of a geo-stationary satellite in its orbit is A . 12 hrs B. 24 hrs c. 365 days D. none of these | 11 |

736 | If a Parrot starts flying upwards with an acceleration in an air tight cage, then the boy will feel the weight of the cage: A. Unchanged B. Reduced c. Increased D. Nothing can be said | 11 |

737 | In CGS, the gravitational unit of force is A. ( k g f ) B. ( N ) ( mathrm{c} cdot g f ) D. dyne | 9 |

738 | Consider two spherical planets of same average density, Planet 2 is 8 limes as massive as planet 1. The ratio ot the acceleration due to gravity on the second planet to that on the first is. ( A ) B. 2 ( c cdot 4 ) D. 8 | 11 |

739 | If the radius of the earth is reduced to half of its present value, with no change in the mass, how will the acceleration due to gravity, be affected? | 11 |

740 | Consider a satellite going round the earth in a circular orbit. Which of the following statements is wrong? A. It is a freely falling body B. It is a moving with constant speed. c. It is acted upon by a force directed away from the centre of the earth which counter- balances the gravitational pull. D. Its angular momentum remains constant | 11 |

741 | A thin rod length L is bent to form a circle. Its mass is M. What force will act on the mass ( mathrm{m} ) placed at the center of the circle? A ( cdot frac{4 pi^{2} G M m}{L^{2}} ) B. ( frac{G M m}{4 pi^{2} L^{2}} ) c. ( frac{2 pi G M m}{L^{2}} ) D. zero | 11 |

742 | The orbital speed ( v ) of each moon, such that they maintain the triangular configuration is: A ( cdot sqrt{frac{G M}{R^{2}}+frac{G m}{sqrt{3} R}} ) B. ( sqrt{frac{G M}{R}+frac{G m}{sqrt{3} R}} ) ( ^{mathrm{c}} cdot sqrt{frac{G M^{2}}{R}+frac{G m}{sqrt{3} R}} ) D. ( sqrt{frac{G M}{R}+frac{G m^{2}}{3 R}} ) | 11 |

743 | Velocity of the planet is minimum at A ( . C ) в. ( D ) ( c . A ) ( D ) | 11 |

744 | An astronaut, inside an earth satellite, experiences weightlessness because This question has multiple correct options A. no external force is acting on him B. he is falling freely C. no reaction is exerted by the floor of the satellite D. he is far away from the earth’s surface | 11 |

745 | Calculate the value of the acceleration due to gravity at a place ( 3,200 k m ) above the surface of the earth. | 11 |

746 | the value of ( g ) at the surface of the earth is ( 9.8 m / s^{2} . ) then the value of ( g ) at the place ( 480 k m ) above the surface of the earth will be nearly? (Radius of the earth is ( 6400 k m ) | 11 |

747 | The gravitational potential is a A. scalar B. vector C. scalar based on the mass of the particle D. scalar or vector depending on the situation | 11 |

748 | The escape velocity of a projectile from the earth’s surface is approximately. A. ( 7 mathrm{km} / mathrm{s} ) В. ( 112 mathrm{km} / mathrm{s} ) c. ( 11.2 mathrm{km} / mathrm{s} ) D. ( 1.1 mathrm{km} / mathrm{s} ) | 11 |

749 | A body is taken to a height of ( n R ) from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is A ( cdot(n+1)^{2} ) B ( cdot(n+1)^{-2} ) c. ( (n+1)^{-1} ) D. ( (n+1) ) | 11 |

750 | How much would a W kg man weigh on the moon in terms of gravitational units? A ( cdot frac{W}{6} ) kg-wt B. 6W kg-wt c. w kg-wt D. zero | 9 |

751 | Suppose the acceleration due to gravity at the earth’s surface is ( 10 mathrm{m} / mathrm{s}^{2} ) and at the surface of mars it is ( 4.0 mathrm{m} / mathrm{s}^{2} . ) A ( 60 mathrm{kg} ) passenger goes from the earth to the mars in a spaceship moving with a constant velocity. Neglect all other object in the sky. Which part of the figure best represent the weight (net gravitational force) of the passenger as a function of time? ( A cdot A ) В. ( B ) ( D ) | 11 |

752 | Two planets revolves around the sun with frequencies ( N_{1} ) and ( N_{2} ) revolutions per year. If their average radii (orbital) be ( R_{1} ) and ( R_{2} ) respectively, then ( R_{1} / R_{2} ) is equal to: A ( cdotleft(N_{1} / N_{2}right)^{2 / 3} ) a B . ( left(N_{1} / N_{2}right)^{3 / 2} ) C ( cdotleft(N_{2} / N_{1}right)^{2 / 3} ) D. ( left(N_{2} / N_{1}right)^{3 / 2} ) | 11 |

753 | The value of ‘g’ at the depth from the ground goes on A. increasing B. fluctuating c. decreasing D. varying | 11 |

754 | If the density of the earth is doubled to that of its original value, the radius remaining the same, what will be the change in acceleration due to gravity? | 11 |

755 | At which height from the earth’s surface, acceleration due to gravity is decreased by ( 75 % ) of its value at earth’s surface. | 11 |

756 | Two spherical bodies of mass ( M ) and ( 5 M ) and radii ( R ) and ( 2 R ) respectively are released in free space with initial separation between their centres equal to ( 12 R ) If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is A . ( 2.5 R ) в. ( 4.5 R ) ( c .7 .5 R ) D. ( 1.5 R ) | 11 |

757 | A semicircular wire.has a length L and mass M.A particle of mass m is placed at the center of the circle. Find the gravitational attraction on the particle due to the wire. | 11 |

758 | Kepler’s second law is based on: A. Newton’s first law B. Newton’s second law C . special theory of relativity D. conservation of angular momentum | 11 |

759 | Weight of a body of mass m decreases by ( 1 % ) when it is raised to height ( h ) above the Earth’s surface. If the body is taken to a depth h in a mine, then its weight will: A. Decreases by ( 0.5 % ) B. Decreases by ( 2 % ) c. Increases by ( 0.5 % ) D. Increase by ( 1 % ) | 11 |

760 | Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and stars is proportion to ( R_{1} / 2, ) there ( T^{2} ) is proportional to. A ( cdot R^{2} ) B . ( R^{1 / 2} ) c. ( R^{-1 / 2} ) D. ( R^{1} / 3 ) | 11 |

761 | The percentage change in the acceleration of the earth towards the sun from a total eclipse of the sun to the point where the moon is on a side of earth directly opposite to the sun is: ( r_{1} ) is the distance of earth from sun, ( r_{2} ) is the distance of earth from moon A ( cdot frac{M_{s}}{M_{m}} frac{r_{2}}{r_{1}} times 100 ) B. ( frac{M_{s}}{M_{m}}left(frac{r_{2}}{r_{1}}right)^{2} times 100 ) ( ^{mathbf{C}} 2left(frac{r_{1}}{r_{2}}right)^{2} frac{M_{m}}{M_{s}} times 100 ) ( ^{mathrm{D}}left(frac{r_{1}}{r_{2}}right)^{2} frac{M_{s}}{M_{m}} times 100 ) | 11 |

762 | If the inertial mass ( m_{i} ) of the bob of a simple pendulum of length ( ; l^{prime} ) is not equal to the gravitational mass ( m_{g} ) then its time period is: ( ^{mathrm{A}} cdot_{T}=2 pi sqrt{frac{m_{i} l}{m_{g} cdot g}} ) В ( cdot T=2 pi sqrt{frac{m_{g} cdot l}{m_{i cdot g}}} ) ( ^{mathbf{c}} cdot_{T}=2 pi sqrt{frac{l}{g}} ) ( ^{mathrm{D}} cdot_{T}=2 pi sqrt{frac{left(m_{i}+m_{g}right)}{left(m_{i}-m_{g}right)} cdot frac{l}{g}} ) | 11 |

763 | Two planets, ( A ) and ( B ), orbit a star. Planet A moves in an elliptical orbit whose semi major axis has length a. Planet B moves in an elliptical orbit whose semi major axis has a length of 9a. If planet ( A ) orbits with a period ( T, ) what is the period of planet Bs orbit? A. 7297 в. 27 T ( c cdot 3 T ) D. ( T / 3 ) E. т/27 | 11 |

764 | A body weighs ( 36 k g ) on the surface of the Earth. How much would it weights on the surface of a planet,whose mass is ( frac{1}{9} ) and radius ( frac{1}{3} ) of that of earth? | 11 |

765 | Mass of the earth is 81 times the mass of the moon and distance between the earth and moon is 60 times the radius of the earth. If ( R ) is radius of the earth, then the distance between moon and the point on the line joining the moon and the earth where the gravitation force becomes zero is A. 30R в. 15R ( c cdot 6 R ) D. 5R | 11 |

766 | A particle of mass ( M ) is placed at the centre of a uniform spherical shell of mass ( 2 M ) and radius The gravitational potential on the surface of the shell is: A. ( -frac{G M}{R} ) в. ( -frac{3 G M}{R} ) c. ( -frac{2 G M}{R} ) D. zero | 11 |

767 | Two identical particles of mass ( 1 mathrm{kg} ) experience a gravitational force of 10N between them . The distance between them is r. If the same setup is put in water (refractive index ( =1.5 ) ), how will their gravitational force change A. The gravitational force will reduce to 1 N B. The gravitational force remains constant c. The gravitational force becomes ( 20 / 3 mathrm{N} ) D. The gravitational force becomes 15 N | 11 |

768 | The radii of two planets are respectively ( R_{1} ) and ( R_{2} ) and their densities are respectively ( rho_{1} ) and ( rho_{2} . ) The ratio of the accelerations due to gravity at their surfaces is A ( cdot g_{1}: g_{2}=frac{rho_{1}}{R_{1}^{2}}: frac{rho_{2}}{R_{2}^{2}} ) ( mathbf{B} cdot g_{1}: g_{2}=R_{1} R_{2}: rho_{1} rho_{2} ) ( mathbf{c} cdot g_{1}: g_{2}=R_{1} rho_{1}: R_{2} rho_{1} ) ( mathbf{D} cdot g_{1}: g_{2}=R_{1} rho_{1}: R_{2} rho_{2} ) | 11 |

769 | The acceleration due to gravity at the poles and the equator is ( g_{p} ) and ( g_{e} ) respectively. If the earth is a sphere of radius ( R_{E} ) and rotating about its axis with angular speed ( omega, ) then ( g_{p}-g_{e} ) is then given by ( ^{mathrm{A}} cdot frac{omega^{2}}{R_{E}} ) B. ( frac{omega^{2}}{R_{E}^{2}} ) c. ( omega^{2} R_{E}^{2} ) D. ( omega^{2} R_{E} ) | 11 |

770 | Consider earth to be a homogeneous sphere. Scientist ( boldsymbol{A} ) goes deep down in a mine and scientist ( B ) goes high up in a balloon. The gravitational field measured by A. ( A ) goes on decreasing and that by ( B ) goes on increasing B. ( B ) goes on decreasing and that by ( A ) goes on increasing c. Each decreases at the same rate D. Each decreases at different | 11 |

771 | A particle of mass ( mathrm{M} ) is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre will be : ( A cdot frac{G M}{a} ) B. ( frac{2 G M}{a} ) ( mathrm{c} cdot frac{3 G M}{a} ) D. ( frac{4 G M}{a} ) | 11 |

772 | Find the height from the earth’s surface where ( g ) will be ( 25 % ) of its value on the surface of earth ( (mathrm{R}=mathbf{6 4 0 0} mathrm{km}) . ) (b) Find the percentage increase in the value of ( mathrm{g} ) at a depth h from the surface of earth. | 11 |

773 | Average density of the earth A. does not depend on g B. is a complex function of ( g ) C. is directly proportional to ( g ) D. is inversely proportional to g | 11 |

774 | Assertion Kepler’s second law can be understood by conservation of angular momentum principle. Reason Kepler’s second law is related with areal velocity which can further be proved to be based on conservation of angular momentum as ( (boldsymbol{d A} / boldsymbol{d t})=left(boldsymbol{r}^{2} boldsymbol{omega}right) / 2 ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect and Reason is correct | 11 |

775 | If a planet of given density were made larger, its force of attraction for an object on its surface would increase because of the greater distance from the object to the centre of the planet. Which effect predominates? | 11 |

776 | If ( W_{1}, W_{2} ) and ( W_{3} ) represent the work done in moving a particle from ( boldsymbol{A} ) to ( boldsymbol{B} ) along three different paths 1,2 and 3 respectively (as shown) in a gravitational field of point mass ( boldsymbol{m} ) then find the correct relation between ( W_{1}, W_{2} ) and ( W_{3} ) A ( . W_{1}=W_{2}=W_{3} ) B. ( W_{1}>W_{2}>W_{3} ) ( mathbf{c} cdot W_{1}<W_{2}W_{1}>W_{3} ) | 11 |

777 | Which of the following doesn’t show that air has pressure? A. Ball falling to the ground B. Flying a kite c. Riding a bicycle against the wind D. none of these | 11 |

778 | Given that ( T ) stands for time period and stands for the length of simple pendulum. If ( g ) is the acceleration due to gravity, then which of the following statements about the relation ( boldsymbol{T}^{2}= ) ( (l / g) ) is correct? A. It is correct both dimensionally as well as numerically y B. It is neither dimensionally correct nor numerically. c. It is dimensionally correct but not numerically. D. It is numerically correct but not dimensionally. | 11 |

779 | The gravitational force with which the earth attracts the moon: A. is less than the force with which the moon attracts the earth ( mathbf{B} ). is equal to the force with which the moon attracts the earth c. is greater than the force with which the moon attracts the earth D. varies with the phases of the moon | 9 |

780 | Escape velocity of a particle depends on its mass ( mathbf{A} cdot m^{2} ) в. ( m ) ( mathrm{c} cdot m^{0} ) D. ( m^{-1} ) | 11 |

781 | The earth ( left(operatorname{mas} s=6 times 10^{24} k gright) ) revolves around the sun with an angular velocity of ( 2 times 10^{-7} ) radian/sec in a circular orbit of radius ( 1.5 times 10^{8} k m . ) The force exerted by the sun, on the earth is :- A ( cdot 6 times 10^{19} N ) B . ( 18 times 10^{25} N ) c. ( 36 times 10^{21} N ) D. ( 27 times 10^{39} N ) | 11 |

782 | Assertion A planet moves faster, when it is closer to the sun in its orbit and vice versa Reason Orbital velocity for an orbiting planet is constant A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

783 | Two point object of masses ( 10^{4} k g, 10^{6} k g ) are ( 1.2 times 10^{3} m ) apart. Find distance of point from smaller mass at which the net gravitational force due to them will be zero(in m) A . 109 B. 1100 ( c cdot 11 ) D. 99 | 9 |

784 | A satellite is in a circular orbit around a planet, Its period of revolution is ( mathrm{T} ), radius of the orbit is ( R ), orbital velocity ( V ) and acceleration ‘a’, then: A ( cdot V=a t ) and ( a=frac{V^{2}}{R} ) B. ( V=frac{2 pi R}{T} ) and ( V=a T ) c. ( V=frac{2 pi R}{T} ) and ( a=frac{V^{2}}{R} ) D. ( V=frac{1}{2} a T^{2} ) | 11 |

785 | The speed of the earth is highest when it is A. Farthest from the sun B. Nearest to the sun c. Passing through the month of September D. None of the above | 11 |

786 | Assertion Many great rivers flow towards the equator. The sediments that they carry increase the time of rotation of the earth about its own axis. Reason The angular momentum of the earth about its rotation axis is conserved. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

787 | What is the value of acceleration due to gravity at height equal to half the radius of earth from surface of earth. [take ( left.g=10 m / s^{2} text { at earth surface }right] ) | 11 |

788 | The value of ( g ) near the earth’s surface is A ( cdot 8.9 m / s^{2} ) в. ( 8.9 m / s ) ( mathrm{c} cdot 9.8 mathrm{m} / mathrm{s}^{2} ) D. ( 9.8 m / s ) | 11 |

789 | A body weighs ( 60 mathrm{kg} ) on the earth’s surface. What would be its weight at the centre of the earth? A. 60 kg-wt B. 6 kg-wt c. ( 60 times 9.8 mathrm{kg} ) -wt D. zero | 11 |

790 | If a ball is projected with a velocity equal to ( 1 / 4 ) th of the escape velocity from the surface of the earth. the height it will attain is ( _{-} ). Radius of Earth] A ( cdot frac{R}{4} ) в. ( frac{R}{32} ) c. ( 4 R ) D. ( frac{R}{16} ) | 11 |

791 | The angular speed of rotation of earth about its axis at which the weight of man standing on the equator becomes half of its weight at the poles is given by: A. 0.034 rads( ^{-1} ) B. ( 8.75 times 10^{-4} )rads( ^{-1} ) c. ( 1.23 times 10^{-2} mathrm{rads}^{-1} ) D. ( 7.65 times 10^{-7} )rads( ^{-1} ) | 11 |

792 | To overcome the effect weightlessness in an artificial satellite A. the satellite is rotated around its axis with compartment of astronaut at the centre of the satellite. B. the satellite is shaped like wheel. C. the satellite is rotated around and around till weightlessness disappears. D. the compartment of astronaut is kept on the periphery of rotating wheel like satellite. | 11 |

793 | State whether true or false. As the distance of the planet from the sun increases, the period of revolution decreases. A. True B. False | 11 |

794 | A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth A. the acceleration of S is always directed towards the centre of the earth B. the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant C. the total mechanical energy of S varies periodically with time D. the linear momentum of S remains constant in magnitude | 11 |

795 | Gravitational acceleration on the surface of a planet is ( frac{sqrt{mathbf{6}}}{11} ) g, where ( g ) is the gravitational acceleration on the surface of the earth. The average mass density of the planet is ( frac{2}{3} ) times that of the Earth. If the escape speed on the surface of the earth is taken to be 11 ( k m s^{-1}, ) the escape speed on the surface of the planet is ( k m s^{-1} ) will be? | 11 |

796 | The depth at which the value of ( g ) becomes ( 25 % ) of that at the surface of the earth is (in ( mathrm{Km} ) ) ( A cdot 4800 ) B. 2400 c. 3600 D. 1200 | 11 |

797 | The distance of Neptune and Saturn from the sun are nearly ( 10^{13} mathrm{m} ) and ( 10^{12} ) ( mathrm{m} ) respectively. Assuming that they move in circular orbits, their periodic times would be in the ratio of A . 10 в. 100 c. ( 10 sqrt{10} ) D. 1000 | 11 |

798 | Two spheres each of mass ( 10^{5} k g ) and radius ( 10 m ) are kept in constant. Find the force of gravitational acting between them. ( mathbf{A} cdot 10^{-3} N ) В ( cdot 6.67 times 10^{-3} N ) c. ( 6.67 times 10^{-11} N ) D. ( 10^{-11} N ) | 11 |

799 | The moon’s radius is ( frac{1}{4} ) that of the earth and its mass is ( frac{1}{80} ) times that of the earth. If ( g ) represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is A. ( frac{g}{4} ) в. ( frac{g}{5} ) c. ( frac{g}{6} ) D. ( frac{g}{8} ) | 11 |

800 | Kepler’s second law is a consequence of A. conservation of energy B. conservation of linear momentum C. conservation of angular momentum D. conservation of mass | 11 |

801 | If the radius of the Earth were increased by a factor of 2 and its mass remained the same, then the acceleration due to gravity on the Earth would A. reduce by factor 4 B. reduce by factor 2 c. not change D. none of the above | 11 |

802 | The value of acceleration due to gravity, at earth surface is ( g ). Its value at the centre of the earth, which we assume as a.sphere of radius ( R ) and of uniform mass density, will be: ( mathbf{A} cdot 10 R m / s^{2} ) B. zero c. ( 5 R m / s ) D. ( 20 R m / s^{2} ) | 11 |

803 | The gravitational force between two bodies is A. repulsive at large distances B. attractive at all places c. attractive at short distances D. repulsive at short distances | 9 |

804 | Potential due to a point mass ( m ) at a distance ( r ) is ( V=-frac{G M}{r} ) | 11 |

805 | The gravitational P.E. of a rocket of mass ( 100 mathrm{kg} ) at a distance of ( 10^{7} mathrm{m} ) from the earths centre is ( -4 times 10^{9} ) J. The weight of the rocket at a distance of ( 10^{9} mathrm{m} ) from the centre of the earth is : A ( cdot 4 times 10^{-2} mathrm{N} ) В. ( 4 times 10^{-9} mathrm{N} ) c. ( 4 times 10^{-6} mathrm{N} ) D. ( 4 times 10^{-3} mathrm{N} ) | 11 |

806 | If the distance between the earth and sun were to be doubled from its present value, the number of days in a year would be : A . 64.5 в. 1032 ( c cdot 182.5 ) D. 730 | 11 |

807 | An artificial satellite is revolving round the earth. The radius of its circular orbit is half the orbital radius of moon. The time taken by this satellite in completing one revolution will be A. 2 lunar months B ( cdot 2^{-2 / 3} ) lunar months ( mathrm{c} cdot 2^{-3 / 2} ) lunar months D. ( 1 / 2 ) lunar months | 11 |

808 | The escape velocity for the earth is ( v_{e} ) The escape velocity for a planet whose radius is four times and density is nine times that of the earth, is : A. ( 36 v_{e} ) B. ( 12 v_{e} ) ( c cdot 6 v_{e} ) D. ( 20 v_{c} ) | 11 |

809 | Average density of the earth A. does not depend on ( g ) B. is a complex function of ( g ) C. is directly proportional to ( g ) D. is inversely proportional to ( g ) | 11 |

810 | The magnitude of acceleration due to gravity decreases A. as the height from the surface of the earth increases B. as the depth from the surface of the earth increases C. as one moves from the pole of the earth to its equator D. All the above | 11 |

811 | If the distance between the Sun and Earth is increased by three times then attraction between two will: A. decreases by ( 11 % ) B. decreases by 33% c. decreases by 66% D. decreases by 89% | 11 |

812 | A point mass ( m_{0} ) is placed at a distance ( boldsymbol{R} ) ( frac{n}{3} ) from the centre of a spherical shell of mass ( M ) and radius ( R ). The gravitational force on the point mass ( boldsymbol{m}_{0} ) is: ( ^{mathrm{A}} cdot frac{9 G M m_{0}}{R^{2}} ) в. ( frac{G M m_{0}}{R^{2}} ) c. zero D. ( frac{4 G M m_{0}}{R^{2}} ) | 11 |

813 | A body falls freely towards the earth with: A. uniform speed B. uniform velocity c. uniform acceleration D. none of these | 11 |

814 | If the mass of the earth is doubled and the distance of the moon revolving around the earth is also doubled, then, find the new time period of revolution of moon. (Take the present time of revolution as 28 days) ( A cdot 6 ) B. 36 ( c .56 ) D. 112 | 11 |

815 | A satellite of mass ( 250 k g ) is orbiting the Earth a height of ( 500 k m ) above the surface of Earth. How much energy must be expended to rocket the satellite out of the gravitational influence of the Earth ? Given mass of the Earth ( =6.0 times 10^{24} ) kgradius of the Earth ( =6400 mathrm{km} ; ) and ( mathrm{G}=6.67 mathrm{x} ) ( 10^{-11} N m^{2} k g^{-2} ) | 11 |

816 | The square of its period of revolution around the sun is the cube of the mean distance of a planet from the sun A. Inversely proportional B. Directly proportional c. Not proportional D. depend | 11 |

817 | Newton said that an apple falls down from a tree because A. Apple exerts a force of attraction on the earth B. The earth exerts a force of attraction on the apple c. Both are true D. None of the options are correct | 11 |

818 | A satellite has a kinetic energy ( X ) potential energy ( Y ) and total energy ( z ) in a given orbit. How are they related A. ( Z=Y=-2 X ) в. ( Z=Y / 2=-X ) c. ( Z=2 Y=-2 X ) D. ( 2 Z=Y=-2 X ) ( X ) | 11 |

819 | A mass ( M ) is split into two parts ( m ) and ( (M-m) ) which are then separated by a certain distance. The ratio ( boldsymbol{m} / boldsymbol{M} ) which maximizes the gravitational force between the parts is A . 1: 4 B. 1: 3 c. 1: 2 D. 1: 1 | 11 |

820 | The escape velocity on the earth is ( 11.2 k m / s . ) A planet has twice the radius of earth and same mean density as earth Then the escape velocity on planet in ( k m / s ) will be : A . 5.6 B. 11.2 c. 22.4 D. 16.5 | 11 |

821 | If Earth is supposed to be a sphere of radius ( R, ) if ( g_{30^{circ}} ) is value of acceleration due to gravity at latitude of ( 30^{circ} ) and ( g ) at the equator, the value of ( g-g_{30^{circ}} ) is A ( cdot frac{1}{4} omega^{2} R ) в. ( frac{3}{4} omega^{2} R ) c. ( omega^{2} R ) D. ( frac{1}{2} omega^{2} R ) | 11 |

822 | The largest and the shortest distance of the earth from the sun are ( r_{1} ) and ( r_{2} ). Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun is: A ( cdot frac{r_{1}+r_{2}}{4} ) в. ( frac{r_{1}+r_{2}}{r_{1}-r_{2}} ) c. ( frac{2 r_{1} r_{2}}{r_{1}+r_{2}} ) D. ( frac{r_{1}+r_{2}}{3} ) | 11 |

823 | A hypothetical planet has density ( rho ) radius ( mathrm{R} ), and surface gravitational acceleration ( g ). If the radius of the planet were doubled, but the planetary density stayed the same, find the acceleration due to gravity at the planet’s surface. A ( .4 g ) в. ( 2 g ) ( c . g ) D. ( g / 2 ) | 11 |

824 | Two objects have the same mass and are located near each other at a distance (r). If the mass of one of the objects is doubled and the mass of the other object is tripled, Find out the change in gravitational attraction between them? A. Decrease by ( 1 / 6 ) B. Decrease by ( 2 / 3 ) c. Increase by ( 3 / 2 ) D. Increase by 5 E. Increase by 6 | 11 |

825 | Motion of artificial satellite around the earth is powered by : A . Liquid fuel B. Solar energy c. Atomic energy D. None of these | 11 |

826 | Two satellites of identical masses orbit the earth at different heights. The ratio of their distances from the centre of earth is ( d: 1 ) and the ratio of the acceleration due to gravity at those height is ( g: 1 . ) Then find the ratio of their orbital velocities. A ( cdot sqrt{frac{g}{d}} ) B. ( sqrt{g d} ) ( mathrm{c} cdot sqrt{g} ) D. ( sqrt{g} d ) | 11 |

827 | A student determined to test the law of gravity for himself walks off a skyscraper ( 320 m ) high with a stopwatch in hand and starts his free fall (zero initial velocity). 5 seconds later, superman arrives at the scene and dives off the roof to save the student. what must be superman’s initial velocity in order that he catches the student just before reaching the ground? [assume that superman’s acceleration is that of a free-falling body, ( left.g=10 m / s^{2}right] ) B . ( 25.8 mathrm{ms}^{-1} ) c. ( 4.785 mathrm{ms}^{-1} ) D. Cannot be determined | 11 |

828 | The ratio of the radii of two planets ( r_{1} ) and ( r_{2} ) is ( k . ) The ratio of acceleration due to gravity on them is ( r . ) Then the ratio of the escape velocities from them, will be: A. ( sqrt{frac{r}{k}} ) в. ( sqrt{frac{k}{r}} ) ( c . k r ) D. ( sqrt{k s} ) | 11 |

829 | A satellite is to be placed in equatorial geostationary orbit around earth for communication. The height of such a satellite is ( left[M_{E}=6 times 10^{24} k g, R_{E}=6400 k m, T=right. ) A ( .3 .57 times 10^{5} m ) В. ( 3.57 times 10^{6} m ) c. ( 3.57 times 10^{7} m ) D. ( 3.57 times 10^{8} m ) | 11 |

830 | A saturn year is 29.5 times the earth year. How far is saturn from the moon ( (M) ) if the earth is ( 1.5 times 10^{8} k m ) away from the sun? | 11 |

831 | How is the gravitational force of attraction between two bodies affected if: (i) Mass of both bodies is doubled (ii) The distance between them is halved. | 11 |

832 | Two identical spheres of gold are in contact with each other. The gravitational attraction between them is A. Directly proportional to the square of the radius B. Directly proportional to the cube of the radius C. Directly proportional to the fourth power of the radius D. Inversely proportional to the square of the radius | 11 |

833 | A ball of mass ( mathrm{m} ) is thrown vertically upward from the ground and reaches a height h before momentarily coming to rest.If ( g ) is acceleration due to gravity,the impulse received by the ball due to gravity force during its flight is ( mathbf{A} cdot sqrt{2 m^{2} g h} ) в. ( sqrt{4 m^{2} g h} ) ( mathbf{c} cdot sqrt{8 m^{2} g h} ) D. ( 4 sqrt{m^{2} g h} ) | 11 |

834 | A body weighs ( 72 N ) on the surface of earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface? B. ( 28 N ) ( c .16 N ) D. 32 N | 11 |

835 | If ( R ) is the radius of the earth and ( g ) the acceleration due to gravity on the earth’s surface, then mean density of the earth is: A ( cdot frac{4 pi G}{3 g R} ) в. ( frac{3 pi R}{4 g G} ) c. ( frac{3 g}{4 pi R G} ) D. ( frac{r g}{12 R G} ) | 11 |

836 | Assertion The smaller the orbit of a planet around the Sun, the shorter is the time it takes to complete. Reason According to Kepler’s third law of planetary motion, square of time period is proportional to cube of mean distance from Sun. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

837 | The value of acceleration due to gravity on the surface of the earth depends on. A. pressure B. acceleration c. gravitational force between an object and the earth D. none of these | 11 |

838 | A satellite of mass ‘m’, moving around the earth in a circular orbit of radius ( boldsymbol{R} ) has angular momentum ( L ). The areal velocity of satellite is: ( mathbf{A} cdot L / 2 m ) в. ( L / m ) ( mathbf{c} cdot 2 L / m ) D. ( 2 L / m_{e} ) | 11 |

839 | A man weighs ( 75 k g ) on the surface of the earth. His weight in a geostationary satellite is: A . infinity в. ( 150 k g ) c. zero D. ( 75 / 2 k g ) | 11 |

840 | The mass of the earth is ( 6 times 10^{22} k g ) and that of the moon is ( 7.4 times 10^{22} ) kg. If the distance between the earth and the moon is ( 3.84 times 10^{5} k m, ) calculate the force exerted by the earth on the moon. ( G=6.7 times 10^{-11} N m^{2} k g^{-2} ) | 11 |

841 | Assertion If an object is projected from the earth’s surface with escape velocity, path of the object will be parabola. Reason When object is projected with a velocity less than escape velocity from horizontal surface and greater than orbital velocity, path of the object will be ellipse. A. STATEMENT-1 is True, STATEMENT-2 is True: STATEMENT-2 is a correct explanation for STATEMENT- B. STATEMENT-1 is True, STATEMENT-2 is True: STATEMENT-2 is NOT a correct explanation for STATEMENT-1 c. STATEMENT-1 is True, STATEMENT-2 is False D. STATEMENT-1 is False, STATEMENT-2 is True | 11 |

842 | Two spheres of radius ( r=0.5 mathrm{m} ) and mass 1 kg are placed in contact with each other, what will be the gravitational force between them: A. ( 0 N ),since the spheres are touching each other and ( r=0 ) В. ( 6.67 times 10^{-11} N ) ( mathbf{c} cdot 6.67 times 10^{-4} N ) D. ( 6.67 times 10^{-6} N ) | 11 |

843 | Earth is flattened at poles and bulging at equator. This is due to A. revolution of Earth around the Sun in an elliptical orbit B. angular velocity of spinning about its axis is more at Equator C . centrifugal force is more at Equator than poles D. more centrifugal force at poles than Equator | 11 |

844 | Renu is standing in a dining line ( 6.38 times 10^{4} k m ) from the centre of the earth. The mass of the earth is ( 6 times ) ( 10^{24} k g ) i) Find the acceleration due to gravity ii) Will the value change after she finishes her lunch? | 11 |

845 | Two particles are placed at some distance and the magnitude of gravitational force between them is F. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the new value of gravitational force, in terms of ( F ) between them will be: A ( cdot frac{F}{4} ) в. ( 4 F ) c. ( frac{F}{2} ) D. | 11 |

846 | How does the force of gravitation between two objects change when the distance between them is reduced to half? ( mathbf{A} cdot F^{prime}=4 F ) В . ( F^{prime}=8 F ) ( mathbf{c} cdot F^{prime}=2 F ) D. ( F^{prime}=F ) | 11 |

847 | A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. A. The acceleration of S is always directed towards the centre of earth B. The angular momentum of S about the centre of earth changes in direction but its magnitude remains constant C. The total mechanical energy of S varies periodically with time D. The linear momentum of S remains constant in magnitude | 11 |

848 | A rocket starts vertically upward with speed ( v_{0} . ) Show that its speed ( v ) at height ( h ) is given by ( v_{0}^{2}-v^{2}=frac{2 g h}{1+frac{h}{R}} ) hence ( R ) is the radius of the Earth. | 11 |

849 | Weight of a body on earth’s surface is ( W . ) At a depth half way to the centre of the earth, it will be (assuming uniform density in earth). ( mathbf{A} cdot W ) в. ( W / 2 ) c. ( W / 4 ) D. ( W / 8 ) | 11 |

850 | Fifteen joules of work is done on object A so that only its gravitational potential energy changes. Sixty joules of work is done on object B (same mass as object A) so that only its gravitational potential energy changes. How many times does the height of object B change compared to the height change of object ( A, ) as result of the work done? A. object B changes height four times as much as object A changes height B. Object B changes height sixteen times as much as object A changes height c. object B changes height two times as much as object A changes height D. object B changes height less than two times as much as object A changes height (but not the same amount E. object B changes height the same amount as object changes height | 11 |

851 | If the mass of the earth increases by ( 80 % ) and radius of the earth increases by ( 40 % ) then the percentage charge in acceleration due to gravity on the surface of radius of earth is (where ( g_{s}=frac{G M}{R^{2}}, M= ) mass of earth and ( R= ) radius of earth ( } ) ) A. zero B . ( +8.16 % ) c. ( -8.16 % ) D. ( 160 % ) | 11 |

852 | The dependence of acceleration due to gravity g on the distance r from the centers of the earth assumed to be a sphere of radius ( R ) of uniform density is as shown figure below. The correct figure is ( (i) ) (ii) (iii) (iv) ( A cdot(i) ) B. (ii) ( c ) D. Güvüù | 11 |

853 | Assertion : The acceleration due to gravity on the moon is one-sixth that on the earth. Reason : The law of gravitation is the same on both the moon and the earth. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true and reason is not the correct explanation of assertion. c. If assertion is true but reason is false. D. If both assertion and reason are false | 11 |

854 | If the distance between two masses is doubled, the gravitational attraction between them Is doubled A . Is doubled B. Becomes 4 times c. Is reduced to half D. Is reduced to a quarter | 11 |

855 | In an earth satellite moving in a circular orbit, a piece of metal weighing ( 16 g ) (on the earth) is weighed by a spring balance while the metal is suspended in water. If the relative density of the metal is ( 8, ) what weight will be recorded? A. ( -2 g ) B. zero ( c cdot 2 g ) D. 14 g | 11 |

856 | Two planets are revolving around the Earth with velocities ( v_{1}, v_{2} ) and in radii ( r_{1} ) and ( r_{2}left(r_{1}>r_{2}right) ) respectively. Then A ( cdot v_{1}=v_{2} ) в. ( v_{1}>v_{2} ) c. ( v_{1}<v_{2} ) D. ( frac{v_{1}}{r_{1}}=frac{v_{2}}{r_{2}} ) | 11 |

857 | The gravitational force with which the earth attracts the moon: A. Is less than the force with which the moon attracts the earth B. Is equal to the force with which the moon attracts the earth c. Is greater than the force with which the moon attracts the earth D. Varies with the phases of the moon | 11 |

858 | One mega joule approximately equals ( A cdot 240 mathrm{kcal} ) B. 2400 kcal c. 24 kcasl D. 2.4 kcal | 11 |

859 | Two balls, each of radius ( R ), equal mass and density are placed in contact, than the force of gravitation between them is proportional to ( ^{mathrm{A}} cdot F propto frac{1}{R^{2}} ) в. ( F propto R ) ( c cdot F propto R^{4} ) D. ( F propto frac{1}{R} ) | 9 |

860 | The length of time a satellite takes to orbit the earth depends on its: A. launch speed B. mass c. distance from the earth D. weight E. orbital direction | 11 |

861 | G’ represents I. Mutual conductance II. Gibbs function III. Gravitational constant Which combination is correct? A. Il and III only B. I and III only c. ॥ only D. I, I land III | 11 |

862 | While orbiting around the earth in a spaceship, an astronaut weight becomes A. greater than their real weight B. lesser than their real weight c. zero D. infinity | 11 |

863 | Taking the earth to be a uniform sphere of radius ( 6400 mathrm{km} ) and the value of ( g ) at the surface to be ( 10 mathrm{m} s^{-2} ), calculate the energy needed to raise a satellite of mass ( 2000 mathrm{kg} ) to a height of ( 800 mathrm{km} ) above the earth’s surface and to set it into circular orbit at that altitude. B. ( 8 times 10^{10} ) J. ( mathbf{c} cdot 9 times 10^{10} J ) D. ( 1.8 times 10^{10} ) J. | 11 |

864 | A satellite moving in a circular path of radius ( r ) around earth has a time period T. If its radius slightly increases by ( 4 % ) then percentage change in its time period is: A . ( 1 % ) B. ( 6 % ) c. ( 3 % ) D. ( 9 % ) | 11 |

865 | The gravitational potential at height ( h ) above the earth’s surface is ( -5.12 times ) ( 10^{7} mathrm{J} / mathrm{kg} ) and acceleration due to gravity at this point is ( 6.4 m s^{-2} . ) If radius of the earth is ( 6400 mathrm{km} ), the value of h is : A. ( 1200 mathrm{km} ) B. 1600 km c. ( 1800 mathrm{km} ) D. 2400 km | 11 |

866 | 1 kgf ( = ) ( mathbf{A} cdot 9.8 N ) В. ( 98 N ) c. ( 980 N ) D. none of these | 9 |

867 | The change in the gravitational potential energy when a body of mass ( m ) is raised to a height ( n R ) above the surface of the earth is (here ( R ) is the radius of the earth) A ( cdotleft(frac{n}{n+1}right) m g R ) B ( cdotleft(frac{n}{n-1}right) m g R ) c. ( n m g R ) D. ( frac{m g R}{n} ) | 11 |

868 | At some planet, ( g=1.96 m s^{-2} . ) If it is safe to jump from a height of ( 2 m ) on earth, then the corresponding safe height on that planet is ( mathbf{A} cdot 2 m ) B. ( 5 m ) c. ( 10 m ) D. ( 20 m ) | 11 |

869 | When an object is thrown up from the surface of the earth, the force of gravity: A. acts in the direction of the motion B. acts in the opposite direction of the motion c. remains constant as the body moves up D. increases as the body moves up | 11 |

870 | Two spherical balls of mass 10 kg each are placed ( 10 mathrm{cm} ) apart.Find the gravitational force of attraction between them. | 11 |

871 | The moon revolves round the earth 13 times in one year. If the ratio of sunearth distance to earth-moon distance is ( 392, ) then the ratio of masses of sun and earth will be A . 365 B. 356 c. ( 3.56 times 10^{5} ) D. | 11 |

872 | A point mass ( mathrm{m} ) is placed inside a spherical shell of radius ( mathrm{R} ) and mass ( mathrm{M} ) at a distance ( R / 2 ) from the centre of the shell. The gravitational force exerted by the shell on the point mass is? ( ^{mathbf{A}} cdot frac{G M m}{R^{2}} ) В. ( -frac{G M m}{R^{2}} ) c. zero D. ( _{4} frac{G M m}{R^{2}} ) | 11 |

873 | “Action at a distance” is revealed most prominently in: A. Magnetic force B. Electric force c. Gravitational force D. All of them | 11 |

874 | Two point objects of masses 1.5 g and 2.5 g respectively are at a distance of 16 ( mathrm{cm} ) apart, the centre of gravity is at a distance ( x ) from the object of mass 1.5 g where ( x ) is: ( A cdot 10 mathrm{cm} ) B. ( 6 mathrm{cm} ) ( c cdot 13 mathrm{cm} ) D. 3 cm | 9 |

875 | Sl unit of gravitational constant is: A ( cdot N^{2} m^{2} k g^{2} ) в. ( N m k g^{2} ) c. ( N^{2} m k g^{-2} ) D. ( N m^{2} k g^{-2} ) | 11 |

876 | Universal Gravitational Constant is measured by A. Newton’s Experiment B. Cavendish’s Experiment c. Max’s Experiment D. de Broglie’s Experiment | 11 |

877 | Two celestial bodies are separated by some distance. If the mass of any one of the point like bodies is doubled while the mass of other is halved then how far should they be taken so that the gravitational force between them becomes one-fourth? | 11 |

878 | An artificial satellite revolves around the earth in a circular orbit with a speed v. If ( m ) is the mass of the satellite, its total energy is : A ( cdot frac{1}{2} m v^{2} ) B. ( -frac{1}{2} m v^{2} ) ( mathrm{c} cdot-m v^{2} ) D. ( frac{3}{2} m v^{2} ) | 11 |

879 | State two essential features of a geostationary satellite. | 11 |

880 | A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is ( 11 mathrm{kms}^{-1} ), the escape velocity from the surface of the planet would be A. ( 1.1 mathrm{km} / mathrm{s} ) в. ( 11 mathrm{km} / mathrm{s} ) c. ( 110 mathrm{km} / mathrm{s} ) D. ( 0.11 mathrm{km} / mathrm{s} ) | 11 |

881 | Imagine a new planet having the same density as that of Earth but is 3 times bigger than the Earth in size. If the acceleration due to gravity on the surface of Earth is ( g ) and that on the surface of the new planet is ( g^{prime} ), then: A ( cdot g^{prime}=3 g ) B. ( g^{prime}=frac{g}{9} ) c. ( g^{prime}=9 g ) D. ( g^{prime}=27 g ) | 11 |

882 | The mass of earth is 80 times that of moon and its diameter is double that of moon. If the value of acceleration due to gravity on earth is ( 9.8 m s^{-2} ) then the value of acceleration due to gravity on moon will be? A ( cdot 0.98 mathrm{ms}^{-2} ) В. ( 0.49 mathrm{ms}^{-2} ) c. ( 9.8 mathrm{ms}^{-2} ) D. ( 4.9 mathrm{ms}^{-2} ) | 11 |

883 | The areal velocity of an object of mass ( mathrm{m}=2 mathrm{kg} ) revolving around another object is given by ( 2 m^{2} / s, ) what is the angular momentum of the particle A ( cdot 6 k g-m^{2} / s ) в. ( 8 k g-m^{2} / s ) c. ( 4 k g-m^{2} / s ) D. ( 2 k g-m^{2} / s ) | 11 |

884 | Read the assertion and reason carefully to mark the correct option out of the options given below: Assertion : Radius of circular orbit of a Reason: Areal velocity is given as ( frac{boldsymbol{d} boldsymbol{A}}{boldsymbol{d} boldsymbol{t}}=frac{boldsymbol{L}}{boldsymbol{2 m}}=frac{boldsymbol{m} boldsymbol{v} boldsymbol{r}}{boldsymbol{2} boldsymbol{m}} ) | 11 |

885 | Weightlessness in the satellite is due to A. zero gravitational acceleration B. zero acceleration c. zero mass D. None of these | 11 |

886 | The place where the value of ‘g’ is unaffected by the increase (or) decrease in the speed of rotation of the earth about its own axis is poles A. True B. False | 11 |

887 | Two spheres each of mass ( 10^{5} mathrm{kg} ) and radius ( 10 mathrm{m} ) are kept in contact. Find the force of gravitation acting between them? | 11 |

888 | Two bodies of masses ( m ) and ( 4 m ) are placed at a distance ( r . ) The gravitational potential at a point on the line joining them where the gravitational field is zero is : A . zero B. ( -frac{4 mathrm{Gm}}{mathrm{r}} ) ( c cdot-frac{6 G m}{r} ) D. ( -frac{9 mathrm{Gm}}{mathrm{r}} ) | 11 |

889 | Four similar particles of mass ( mathrm{m} ) are orbiting in a circle of radius ( r ) in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by ( A ) B. ( sqrt{frac{G m}{r}} ) c. ( sqrt{frac{G m}{2}(1+2 sqrt{2})} ) ( frac{1}{2}left[frac{G m}{r}left(frac{1+2 sqrt{2}}{2}right)right]^{frac{1}{2}} ) | 9 |

890 | A mass ( M ) is broken in two parts : ( m ) and (M- m). What would be the relation between ( m ) and ( M ) so that the force of gravitation between the two parts is maximum? A. ( m M=2 ) в. ( m=frac{M}{2} ) ( mathbf{c} cdot M=m^{2} ) D. none of these | 11 |

891 | Imagine a light planet revolving around a very massive star in a circular orbit of radius ( R ) with a period of revolution ( T . ) If the gravitational force of attraction between the planet and the star is proportional to ( R^{-5 / 2}, ) then ( T^{2} ) is proportional to: ( mathbf{A} cdot R^{3} ) B. ( R^{7 / 12} ) c. ( R^{3 / 2} ) D. ( R^{3.75} ) | 11 |

892 | What is difference between ( mathrm{Nm} ) & mN? | 11 |

893 | A satellite of mass ( m ) revolves around the earth of radius ( R ) at a height ( x ) from its surface. If ( g ) is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is A . ( sqrt{g x} ) в. ( sqrt{frac{g R}{R-x}} ) ( ^{mathrm{c}} cdot sqrt{frac{g R^{2}}{R-x}} ) D. ( sqrt{frac{g R^{2}}{R+x}} ) | 11 |

894 | Weight’ of a body may have the following attributes. It is the gravitational force acting on a body at the earth’s surface II. It is independent of the mass of the body III. The body is weightless during free fall IV. It is different at different places on earth’s surface. A . I, Il and III only B . I, III and IV only c. I and III only D. I, II, III and IV | 11 |

895 | Assertion A heavy object always falls faster than a light object when dropped from a height Reason Gravitational force is proportional to the | 11 |

896 | If ( mathrm{M} ) is the mass of the earth and ( mathrm{R} ) its radius, the ratio of the gravitational acceleration and the gravitational constant is given by: A ( cdot frac{R^{2}}{M} ) в. ( frac{M}{R^{2}} ) c. ( M R^{2} ) D. ( frac{M}{R} ) | 11 |

897 | Suppose universal gravitational constant starts of decrease, then This question has multiple correct options A. Length of the day on the earth will increase B. Length of the year will increase c. The earth will follow a spiral path of decreasing radius D. Kinetic energy of the earth will decrease | 11 |

898 | How much would a W kg man weigh on the moon in terms of gravitational units? A ( cdot frac{W}{6} ) kg wt B. 6 W kg wt c. w kg wt D. zero | 9 |

899 | The value of gravitational constant ( boldsymbol{G} ) in Meter-Kilogram-Second system is ( 6.67 times 10^{-11} N-m^{2} k g^{-2} . ) What will be its value in centimetre gram second system. A. ( 6.67 times 10^{-5} ) В. ( 6.67 times 10^{-9} ) ( mathbf{c} cdot 6.67 times 10^{-8} ) D. ( 6.67 times 10^{-13} ) | 9 |

900 | In the figure ( A B=B C, A C=C D ) and ( angle A C D=90^{circ} . ) If the radius of the circle is “r” units then find the length of the chord BC. A ( cdot r sqrt{sqrt{2-1}} ) B ( cdot r sqrt{sqrt{3-1}} ) c. ( r sqrt{2-sqrt{2}} ) D. ( r sqrt{2-sqrt{3}} ) | 11 |

901 | A man covers 60 m distance in one minute on the surface of earth. The distance he will cover on the surface of moon in one minute is ( left(g_{m}=frac{g_{e}}{6}right) ) ( A .60 m ) в. 60 Х 6 т c. ( frac{60}{6} m ) D. ( sqrt{60} m ) | 11 |

902 | An object is dropped at the surface of the earth from the height of ( 3600 mathrm{km} ) Calculate the ratio of the weight of the body at that height and on the surface of the earth. A .1 .34 B . 2.44 ( c .6 .25 ) D. 12.32 | 11 |

903 | Kepler’s second law is based on A. Newton’s first law B. Newton’s second law c. special theory of relativity D. conservation of angular momentum | 11 |

904 | India’s Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at ( mathrm{E} ) and meets Mars at M. If the semi-major axis of Earth’s orbit is ( a_{e}=1.5 times ) ( 10^{11} m, ) that of Mars’s orbit ( a_{m}= ) ( 2.28 times 10^{11} m, ) taken Kepler’s laws, the estimate of time of Mangalyan to reach Mars from Earth to be close to A. 500 days B. 320 days c. 260 days D. 220 days | 11 |

905 | The motion of a planet around sun in an elliptical orbit is shown in the following figure. Sun is situated on one focus. The shaded areas are equal. If the planet takes time ( t_{1} ) and ( t_{2} ) in moving from ( A ) to B and from ( C ) to D respectively then ( mathbf{A} cdot t_{1}>t_{2} ) B . ( t_{1}<t_{2} ) c. ( t_{1}=t_{2} ) D. information incomplete | 11 |

906 | Motion of artificial earth satellites around the earth is powered by A . Liquid fuel B. Solar batteries C. Atomic energy D. None of the above | 11 |

907 | Minimum percentage increase in the kinetic energy of a satellite orbiting close to the surface of the earth so that it will escape the earth’s gravitational pull is A . 50% B. 150% c. ( 100 % ) D. 200% | 9 |

908 | If the distance between the earth and the sun is half its present value, the number of days in a year would have been A. 730 B. 182.5 ( c cdot 129 ) D. 64.5 | 11 |

909 | At what height from the ground will be the value of ( g ) be the same as that in ( 10 k m ) deep mine below the surface of earth. ( A cdot 20 mathrm{km} ) B. 7.5 km ( c cdot 5 k m ) D. 2.5 km | 11 |

910 | A particle of mass ( 1 mathrm{kg} ) is placed at a distance of ( 4 mathrm{m} ) from the centre and on the axis of a uniform ring of mass ( 5 mathrm{kg} ) and radius 3m. The work done to increase the distance of the particle from ( 4 mathrm{m} ) to ( sqrt{3} m ) is. A ( cdot frac{G}{3} J ) в. ( frac{G}{4} J ) c. ( frac{G}{5} J ) D. ( frac{G}{6} J ) | 11 |

911 | A body weighs ( 60 mathrm{kg} ) on the earth’s surface. What would be its weight at the centre of the earth? A. 60 kg-wt B. 6 kg-wt c. ( 60 times 9.8 mathrm{kg} ) -wt D. zero | 11 |

912 | State and explain Universal law of Gravitation. Give its vector form. | 11 |

913 | When a fruit falls from a tree, A. only the earth attracts the fruit B. both the earth and the fruit attract each other C . only the fruit attracts the earth D. they repel each other | 9 |

914 | When a satellite falls to an orbit of smaller radius its kinetic energy: A . Decrease B. Increase c. Remains same D. Nothing can be predicted | 11 |

915 | If velocity of a satellite is half of escape velocity, then distance of the satellite from earth surface will be. A. ( 6400 k m ) B. ( 12800 k m ) c. ( 6400 sqrt{2} k m ) D. ( frac{6400}{sqrt{2}} k m ) | 11 |

916 | Weightlessness experienced while orbiting the earth in a spaceship is the result of A. Inertia B. Accelaration c. zero gravity D. Centre of gravity | 11 |

917 | What is the geometrical interpretation of infinity for gravitational field and gravitational potential? | 11 |

918 | Weightlessness experienced in a spaceship is due to A. absence of of inertia. B. absence of gravity c. absence of accelerating force. D. free fall of the spaceship | 11 |

919 | State whether true or false. The direction of acceleration due to gravity is always vertically downward. A. True B. False | 11 |

920 | A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is ( V ). Due to the rotation of a planet about its axis the acceleration due to gravity ( g ) at equator is ( frac{1}{2} ) of ( g ) at poles. The escape velocity of a particle on the pole of a planet in terms of ( V ) is A ( cdot V_{e}=2 V ) B. ( V_{e}=V ) ( mathrm{c} cdot_{V_{e}}=frac{V}{2} ) D. ( V_{e}=sqrt{3} V ) | 11 |

921 | A planet of mass ( M ) moves around the Sun along an ellipse so that its minimum distance from the Sun is equal to ( r ) and the maximum distance to ( R ) Making use of Kepler’s laws, find its period of revolution around the Sun. | 11 |

922 | The force acting on a mass of 1 g due to the gravitational pull on the earth is called 1 g wt. One ( g ) wt equals A . ( 1 mathrm{N} ) B. 9.8N c. 980 dyne D. None of these | 11 |

923 | Four particles having masses ( mathrm{m}, 2 mathrm{m}, 3 mathrm{m} ) and ( 4 mathrm{m} ) are placed at the four corners of a square of edge a. Find gravitational force acting on a particle of mass ( mathrm{m} ) place at the center. | 11 |

924 | A hole is drilled along the earth’s diameter and a stone is dropped into it. When the stone is at the centre of the earth, it has. A. Acceleration B. Weight c. Mass D. Potential energy | 11 |

925 | If the radius of the earth is increased by three times, keeping the mass constant, then the weight of a body on the earth surface will be as compared to its previous value A . one third B. one ninth c. three times D. nine times | 11 |

926 | Three uniform spheres, each having mass ( mathrm{m} ) and radius ( mathrm{r}, ) are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is? A ( cdot frac{G m^{2}}{r^{2}} ) в. ( frac{G m^{2}}{4 r^{2}} ) c. ( sqrt{2} frac{G m^{2}}{4 r^{2}} ) D. ( sqrt{3} frac{G m^{2}}{4 r^{2}} ) | 11 |

927 | The energy required to remove a body of mass ‘m’ from earths surface is/are equal to: ( mathbf{A} cdot-mathbf{G M m} / mathrm{R} ) в. ( mathrm{mgR} ) c. -mgR D. none of these. | 11 |

928 | The weight of a body at the centre of the earth is A. zero B. Equal to its mass c. Maximum D. Infinite | 11 |

929 | The escape velocity for a rocket on the earth is ( 11.2 mathrm{km} / mathrm{sec} ). Its value on a planet where acceleration due to gravity is twice that on the earth and the diameter of the planet is twice that of the earth, will be (in ( k m / s e c ) ): A . 11.2 B. 5.6 c. 22.4 D. 33.6 | 11 |

930 | A body is weighed by a spring balance to be ( 1000 mathrm{N} ) at the north pole. How much will it weigh(in ( mathrm{N} ) ) at the equator? Account for the earth’s rotation only. | 11 |

931 | In the figure it is shown that the velocity of lift is ( 2 mathrm{ms}^{-1} ) while string ins winding on the motor shaft with velocity ( 2 mathrm{ms}^{-1} ) and shaft ( A ) is moving downward with velocity ( 2 mathrm{ms}^{-1} ) with respect lift, then find out the velocity of block ( mathrm{B} ) ( mathbf{A} cdot 2 mathbf{m s}^{-1} uparrow ) B. ( 2 mathrm{ms}^{-1} downarrow ) ( mathbf{C} cdot 4 mathrm{ms}^{-1} uparrow ) D. None of these | 11 |

932 | A body is suspended from a spring balance kept in a satellite The reading of the balance is ( W_{1} ) when the satellite goes in an orbit of radius ( R ) and is ( W_{2} ) when it goes in an orbit of radius ( 2 R ) Then A. ( W_{1}=W_{2} ) B. ( W_{1}W_{2} ) D. ( W_{1} neq W_{2} ) | 11 |

933 | The force of attraction between two unit point masses separated by a unit distance is called A. Gravitational potential B. Acceleration due to gravity. c. Gravitational field D. Universal gravitational constant. | 11 |

934 | The minimum energy required to launch a ( m ) kg satellite from earth’s surface in a circular orbit at an altitude of ( 2 R ) where ( R ) is the radius of earth, will be: ( mathbf{A} cdot 3 m g R ) в. ( frac{5}{6} ) mg ( R ) c. ( 2 m g R ) D. ( frac{1}{5} m g R ) | 11 |

935 | A planet revolves around the sun in an orbit with an eccentricty ( =0.99, ) the orbit is: A. almost circular B. almost elliptical c. almost straight D. parabolic | 11 |

936 | Figure shows the elliptical path of a planet around the sun. The two shaded parts have equal areas. If ( t_{1} ) and ( t_{2} ) be the time taken by the planet to go from ( a ) to ( b ) and from ( c ) to ( d ) respectively, then ( mathbf{A} cdot t_{1}t_{2} ) D. Insufficient information to deduce the relation between ( t_{1} ) and ( t_{2} ) | 11 |

937 | If earth’s radius were to hypothetically shrink by ( 1 % ), the value of ( G ) would A. shrink by ( 1 % ) B. expand by ( 1 % ) c. remain the same D. shrink by ( 0.01 % ) | 11 |

938 | Planets rotate around the Sun in a path best described as A. elliptical B. circular c. parabola D. none of the above | 11 |

939 | A person sitting in a satellite orbiting earth feels weighlessness due to A. Centripetal acceleration B. Tangential velocity c. Large distance from earth D. zero gravity | 11 |

940 | 1 kgwt is equal to ( mathbf{A} cdot 9.8 N ) B. ( 980 N ) ( mathbf{c} .98 N ) D. none of these | 9 |

941 | Q Type your question- the earth is best represented by ( :(R rightarrow ) Radius of the earth) ( A ) B. ( c ) ( D ) | 11 |

942 | If ( g ) is the acceleration due to gravity on the Earth’ surface, find the gain in potential energy of a body of mass ( m ) when taken from the surface of Earth at a height equal to the radius ( R ) of the Earth. | 11 |

943 | The earth pull all objects towards A. It’s periphery B. It’s centre C. Both centre and periphery D. Earth never pulls any objects.lt is the inbuilt attractive force in a body which attracts it downwards | 11 |

944 | An astronaut who weighs 162 pounds on the surface of the earth is orbiting the earth at a height above the surface of the earth of two earth radii ( (h=2 R ) where ( R ) is the radius of the earth. How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?) A. 81 pounds B. 40.5 pounds c. 18 pounds D. 54 pounds E. 0 pounds (astronaut is weightless | 11 |

945 | tood sonmon voe vourg | 11 |

946 | The gravitational force between two objects placed at a distance r is proportional to ( mathbf{A} cdot r ) в. ( r^{2} ) c. ( frac{1}{r^{2}} ) D. ( frac{1}{r} ) | 11 |

947 | The largest and the shortest distance of the earth from the sun is ( r_{1} ) and ( r_{2} ). Its distance from the sun when it is at perpendicular to the major axis of the orbit drawn from the sun: ( mathbf{A} cdotleft(r_{1}+r_{2}right) / 4 ) B . ( left(r_{1}+r_{2}right) /left(r_{1}-r_{2}right) ) ( mathbf{c} cdot 2 r_{1} r_{2} /left(r_{1}+r_{2}right) ) D. ( left(r_{1}+r_{2}right) / 3 ) | 11 |

948 | (1) Mass of a book is 500 g on thew surface of the earth. what will be its mass at a height equal to radius of earth (2) find the weight of the book at the surface of the earth | 9 |

949 | i) Space Stations are used to study the effects of long-space flight on the human body. Justify. ii) ( boldsymbol{F}=boldsymbol{G} boldsymbol{m}_{1} boldsymbol{m}_{2} / boldsymbol{d}^{2} ) is the mathematical form of Newton’s law of gravitation, ( G- ) gravitational constant ( m_{1} m_{2}, ) are the masses of two bodies separated by a distance ( d ), then given the statement of Newton’s law of gravitation. | 11 |

950 | The mass of the earth is ( 6.00 times 10^{24} k g ) and that of the moon is ( 7.40 times 10^{22} k g ) The constant of gravitation ( G= ) ( 6.67 times 10^{-11} N m^{2} k g^{-2} ). calculate gravitational force of attraction. ( mathbf{A} cdot 38 times 10^{18} ) В. ( 20.2 times 10^{19} ) c. ( 7.60 times 10^{8} ) D. ( 1.90 times 10^{8} ) | 11 |

951 | If the distance between two object in increase two times, they by how many times will the mass of one of the object be change to maintain the same gravitational force? | 11 |

952 | While orbiting around the earth in a apaceship, an astronaut experiences A. more weight B. lesser weight c. weightlessness D. nothing at all | 11 |

953 | When a satellite has an elliptical orbit, the plane of the orbit A. sometimes passes through the centre of earth B. does not pass through the centre of earth c. passes through the centre of earth always D. none of the above | 11 |

954 | A planet has a core and on outer shell of radii ( boldsymbol{R} ) and ( 2 boldsymbol{R} ) respectively. The density of the core is ( x ) and that of outer shell is ( y . ) The acceleration due to gravity at the surface of planet is same as that at depth ( R ) The ratio of ( x ) and ( y ) is ( frac{-}{3} . ) Find ( n ) | 11 |

955 | An extremely small and dense neutron star of mass ( M ) and radius ( R ) is rotating at an angular frequency ( omega . ) If an object is placed at its equator, it will remain stuck to it due to gravity if A ( cdot M>frac{R omega}{G} ) в. ( _{M}>frac{R^{2} omega^{2}}{G} ) ( ^{mathbf{C}} cdot M>frac{R^{3} omega^{2}}{G} ) D. ( M>frac{R^{2} omega^{3}}{G} ) | 11 |

956 | If ( W_{1} ) work is done against gravitational attraction to carry ( 10 mathrm{kg} ) mass from earth’s surface to infinity, then the magnitude of work done by the gravitational attraction in bringing 20 kg mass from infinity to the centre of earth is ( mathbf{A} cdot 2 W_{1} ) в. ( 3 W_{1} ) ( c cdot frac{w_{1}}{2} ) D. ( 4 W_{1} ) | 11 |

957 | If the gravitational constant is expressed in terms of dynesm( ^{-2} boldsymbol{k g}^{2} ) how will the value of G change: A ( .6 .67 times 10^{-11} ) dynes ( k g^{2} m^{-2} ) B . ( 6.67 times 10^{-8} ) dynes ( k g^{2} m^{-2} ) c. ( 6.67 times 10^{-6} ) dynes ( k g^{2} m^{-2} ) D. ( 6.67 times 10^{-3} ) dynes ( operatorname{kg}^{2} m^{-2} ) | 11 |

958 | Calculate the period of revolution of Jupiter around the Sun. The ratio of the radius of Jupiter’s orbit to that of the Earth’s orbit is 5 (Period of revolution of the Earth is 1 year) | 11 |

959 | If the spinning speed of the earth is decreased, then the weight of the body at the poles. A. does not change B. Decresing c. incresing D. may increase and decrease | 11 |

960 | then velocity in circular orbits is given ( operatorname{as} sqrt{frac{boldsymbol{x} boldsymbol{G} boldsymbol{M}}{boldsymbol{r}}} . ) Find ( boldsymbol{x} ) | 11 |

961 | The mass of the moon is about ( 1.2 % ) of the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on earth A. Is the same B. Is smaller c. Is greater D. Varies with its phase | 9 |

962 | Gravitational potential energy is negative. This implies A. Energy is rising along negative ( x ) axis B. A particle is trapped in this potential C. The particle is moving in the opposite direction D. Energy is decreasing in the direction of motion of the particle | 11 |

963 | Two satellites ( A ) and ( B ) of equal mass move in the equatorial plane of the earth, close to earth’s surface. Satellite A moves in the same direction as that of the rotation of the earth while satellite ( mathrm{B} ) moves in the opposite direction. Calculate the ratio of the kinetic energy of ( mathrm{B} ) to that of ( mathrm{A} ) in the reference frame fixed to the earth. ( left(g=9.8 m s^{-2} ) and right. radius of the earth ( =mathbf{6 . 3 7} times mathbf{1 0}^{6} mathbf{k m} ) ). | 11 |

964 | A satellite is revolving in a circular equatorial orbit of radius ( boldsymbol{R}=mathbf{2} times mathbf{1 0}^{mathbf{4}} ) ( mathrm{km} ) from east to west. Calculate the interval after which it will appear at the same equatorial town. Given that the radius of the earth ( =6400 mathrm{km} ) and g(acceleration due to gravity) ( =10 mathrm{m} ) ( s^{-2} ) | 11 |

965 | A planet revolves round the sun in an elliptical orbit of semi minor and major axes ( x ) and ( y ) respectively. Then the time period of revolution is proportional to: A. ( quad(x+y)^{frac{3}{2}} ) в. ( quad(y-x)^{frac{3}{2}} ) c. ( quad_{x} frac{3}{2} ) D. ( frac{3}{y^{frac{3}{2}}} ) | 11 |

966 | If both the mass and radius of the earth decrease by ( 1 % ) the value of This question has multiple correct options A. acceleration due to gravity would decrease by nearly ( % ) B. acceleration due to gravity would increase by 1% c. escape velocity from the earth’s surface would decrease by ( 1 % ) D. the gravitational potential energy of a body on earth’s’s surface will remain unchanged | 11 |

967 | An earth’s satellite moves in a circular orbit with an orbital speed ( 6280 mathrm{ms}^{-1} ) Find the time of revolution. A. 130 min B. 145 min c. 155 min D. 175 min | 11 |

968 | A spaceship is launched into a circular orbit close to earth’s surface. The additional velocity that should be imparted to the spaceship in the orbit to overcome the gravitational pull is: (Radius of earth ( =6400 k m ) and ( g= ) ( mathbf{9 . 8 m} quad boldsymbol{s}^{-1} mathbf{)} ) ( begin{array}{lll}text { A } cdot & 11.2 k m & s^{-1}end{array} ) ( mathbf{B} cdot 8 k m quad s^{-1} ) ( begin{array}{ll}text { c. } 3.2 k m & s^{-1}end{array} ) D. ( 1.5 k m quad s^{-} ) | 11 |

969 | The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately 81 times the mass of the Moon and the distance between the Earth and the Moon is ( 3,85,000 k m . ) A. ( 36,000 mathrm{km} ) from the Moon B. 38,500 km from the Moon. c. ( 34500 mathrm{km} ) from the moon D. 30,000 km from the Moon | 11 |

970 | Two stars of masses ( m_{1} ) and ( m_{2} ) are parts of a binary star system. The radii of their orbits are ( r_{1} ) and ( r_{2} ) respectively, measured from the centre of mass of the system. The magnitude of gravitational force ( boldsymbol{m}_{1} ) exerts on ( boldsymbol{m}_{2} ) is then A. ( frac{m_{1} m_{2} G}{left(r_{1}+r_{2}right)^{2}} ) в. ( frac{m_{1} G}{left(r_{1}+r_{2}right)^{2}} ) c. ( frac{m_{2} G}{left(r_{1}+r_{2}right)^{2}} ) D. ( frac{Gleft(m_{1}+m_{2}right)}{left(r_{1}+r_{2}right)^{2}} ) | 11 |

971 | What is the energy required to move a body of mass ( mathrm{m} ) from orbit of radius ( 2 mathrm{r} ) to ( 3 r ? ) | 11 |

972 | The weight of an object at the centre of the earth of radius R is A. zero B. infinite C . ( R ) times the weight at the surface of the earth D. ( 1 / R^{2} ) times the weight at surface of the earth | 11 |

973 | The rotation of the Earth having radius ( mathrm{R} ) about its axis speed upto a value such that a man at latitude angle ( 60^{circ} ) feels weightless. The duration of the day in such case will be. ( ^{mathrm{A}} cdot_{8 pi} sqrt{frac{R}{g}} ) в. ( 8 pi sqrt{frac{g}{R}} ) ( ^{c} cdot sqrt{frac{R}{g}} ) D. ( 4 pi sqrt{frac{g}{R}} ) | 11 |

974 | If the density of a planet is double than that of the earth and the radius is 1.5 times that of the earth, the acceleration due to gravity on the surface of the planet is ( A ) ( frac{3}{4} ) times that on the surface of earth B. 3 times that on the surface of earth c. ( frac{4}{3} ) times that on the surface of earth D. 6 times that on the surface of earth | 11 |

975 | Figure shows the orbit of a planet ( mathrm{P} ) round the sun ( S . A B ) and ( C D ) are the minor and major axes of the ellipse. If ( t_{1} ) is the time taken by the planet to travel along ( A C B ) and ( t_{2} ) the time along ( B D A ) then: A ( cdot t_{1}=t_{2} ) B ( cdot t_{1}>t_{2} ) ( mathbf{c} cdot t_{1}<t_{2} ) D. nothing can be concluded | 11 |

976 | Q Type your question acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the following table. Least count for length ( =0.1 mathrm{cm}, ) Least count for time ( =0.1 s ) Length of ( quad ) Number of Student Pendulum ( quad ) oscillations ( (n) ) [ begin{array}{l} (mathrm{cm}) \ 64.0 end{array} ] [ 64.0 ] [ 20.0 ] If ( boldsymbol{E}_{boldsymbol{I}}, boldsymbol{E}_{boldsymbol{I I}}, boldsymbol{E}_{boldsymbol{I I I}} ) are the percentage errors in ( g, ) i.e., ( left(frac{Delta g}{g} times 100right) ) for students I, II and III, respectively, then A ( cdot E_{I}=0 ) B. ( E_{I} ) is minimum ( mathbf{c} cdot E_{I}=E_{I I} ) D. ( E_{I I} ) is maximum | 11 |

977 | If a rock is brought from the surface of the moon A. its mass will change B. its weight will change, but not mass c. both mass and weight will change D. its mass and weight will remain the same | 9 |

978 | When a body is at a depth ‘d’ from the earth surface its distance from the centre of the earth is A ( cdot(R-d) ) В. ( 2(R-d) ) c. ( (3 R-d) ) D. ( (R-2 d) ) | 11 |

979 | An iron sphere of mass ( 10 mathrm{kg} ) has the same diameter as an aluminium sphere of mass is ( 3.5 mathrm{kg} ) Both spheres are dropped simultaneously from a tower. When they are ( 10 mathrm{m} ) above the ground, they have the same A. acceleration B. momenta c. potential energy D. kinetic energy | 11 |

980 | As the planet revolves from point ( mathrm{P} ) to point ( Q, ) the velocity of the planet. A. Increases B. Decreases c. Remains same D. Equal is magnitude and opposite in direction | 11 |

981 | Acceleration due to gravity on moon is 0.166 times than that on the earth. ( A ) man weighing 60kg on earth would weigh ( _{text {十一一一一一一一一一 }} ) on moon A. ( 60 mathrm{kg} ) в. 30kg c. ( 16.6 mathrm{kg} ) D. ( 10 mathrm{kg} ) | 11 |

982 | The weight of a person on earth is ( 600 N . ) His weight on moon will appear as: A . zero B. ( 100 N ) c. ( 600 N ) D. 3600 N | 9 |

983 | Kepler’s third law states that square of period of revolution ( (boldsymbol{T}) ) of a planet around the sun, is proportional to third power of average distance ( r ) between sun and planet i.e ( T^{2}=K r^{3} ) here ( K ) is constant. If the masses of sun and planet are ( boldsymbol{M} ) and ( m ) respectively than as per Newton’s law of gravitation force of attraction between them is ( boldsymbol{F}=frac{boldsymbol{G} boldsymbol{M} boldsymbol{m}}{boldsymbol{r}^{2}}, ) here ( boldsymbol{G} ) is gravitational constant The relation between ( G ) and ( K ) is described as A. ( K=G ) B. ( quad K=frac{1}{G} ) c. ( G K=4 pi^{2} ) D. ( G M K=4 pi^{2} ) | 11 |

984 | The value of universal gravitational constant ( G ) is- A. ( 6.67 times 10^{-11} frac{N m^{2}}{k g} ) в. ( 6.67 times 10^{-11} frac{N m^{2}}{k g^{2}} ) c. ( 66.7 times 10^{-11} frac{N m^{2}}{k g^{2}} ) D. ( _{66.7} times 10^{-11} frac{N m^{2}}{k g} ) | 11 |

985 | The ratio of acceleration due to gravity at a depth ( h ) below the surface of earth and at a height ( h ) above the surface for ( boldsymbol{h}<<boldsymbol{R} ) A. is constant B. increases linearly with h. c. varies parabolically with h. D. decreases. | 11 |

986 | The value of acceleration due to gravity at a height ( R ) from surface of the earth is then(R=radius of the earth and geacceleration due to gravity on earth surface ( mathbf{A} cdot mathbf{0} ) в. ( sqrt{g} ) c. ( frac{g}{4} ) D. ( frac{g}{2} ) | 11 |

987 | State whether the given statement is True or False : The value of G depends upon the mass of the two objects. | 11 |

988 | When a small mass ( m ) is suspended at lower end of the elastic wire having upper end fixed with ceiling. There is loss in gravitational potential energy. let it be ( x, ) due to extension of wire, mark correct option, A. The lost energy can be recovered B. The lost energy can be irrecoverable C . only ( frac{x}{2} ) amount of energy recoverable D. only ( frac{x}{3} ) amount of energy recoverable | 11 |

989 | The mean distance of Jupiter from the sun is nearly 5.2 times the corresponding distance between earth and sun. Using Kepler’s Law, find the period of revolution of Jupiter in its orbit. | 11 |

990 | Two particles of masses ( m ) and ( M ) are initially at rest at an infinite distance apart. They move towards each other and gain speeds due to gravitational attraction. Find their speeds when the separation between the masses becomes equal to ( d ) | 11 |

991 | Gravitational potential energy of interaction of a system of two particles of masses ( m_{1} ) and ( m_{2} ) separated by a distance ( r ) ( U=-frac{G m_{1} m_{2}}{r} ) | 11 |

992 | The length of the day from today when the sun is directly overhead till tomorrow again when the sun is directly overhead can be determined by the A. rotation of earth about its own axis B. revolution of earth around sun c. inclination of axis of rotation of earth from the plane of revolution. D. rotation of earth about its own axis as well as its revolution around sun | 11 |

993 | What should be the initial downward speed of the racketeer so that he catches the student at the top of 100 th floor for safe landing? A. It can have many values B . ( 180 mathrm{ms}^{-1} ) c. ( 137.1 mathrm{ms}^{-1} ) D. cannot be determined | 11 |

994 | The masses and the radii of the earth and the moon are ( M_{1}, R_{1} ) and ( M_{2}, R_{2} ) respectively. Their centres are at a distance ( d ) apart. Find the minimum speed with which a particle of mass ( boldsymbol{m} ) should be projected from a point midway between the two centres so as to escape it to infinity. | 11 |

995 | A planet was suddenly stooped in its orbit supposed to be circular. The time it will fall on to the sun is, if time period of planet’s revolution is ( T ) A ( cdot frac{T}{2} ) в. ( frac{sqrt{2} T}{4} ) c. ( frac{sqrt{2} T}{8} ) D. ( sqrt{2} T ) | 11 |

996 | A body falls through a distance ‘h’ in a certain time on the earth. Then if the same body is related on another planet having mass and radius twice as that of the earth, the distance through which it falls in the same time is: ( A cdot frac{h}{2} ) в. ( 2 h ) ( c cdot h ) D. ( 4 h ) | 11 |

997 | What is the magnitude of the gravitational force between the Earth and ( 1 k g ) object on its surface? (Mass of the Earth is ( 6 times 10^{24} k g ) and radius of the Earth is ( 6.4 times 10^{6} m ) A. 9.770 B. 10 N ( c cdot 9 N ) D. 9.5 N | 11 |

998 | The earth’s radius is ( mathrm{R} ) and acceleration due to gravity at its surface is g. If a body of mass ( m ) is sent to a height ( h= ) ( boldsymbol{R} ) ( frac{i}{5} ) from the earth’s surface, the potential energy increases by A . mgh в. ( frac{4}{5} m g h ) c. ( frac{5}{6} ) mgh D. ( frac{6}{7} ) mgh | 11 |

999 | Astronauts on the orbiting space station are weightless because… A. there is no gravity in space and they do not weigh anything. B. space is a vacuum and there is no gravity in a vacuum. C. space is a vacuum and there is no air resistance in a vacuum D. None of the reasons given above are correct | 11 |

1000 | Acceleration due to gravity at surface of a planet is equal to that at surface of the earth and density is 1.5 times that of earth. if radius of earth is ( R ), radius of planet is A ( cdot frac{R}{1.5} ) в. ( frac{2}{3} R ) c. ( frac{9}{4} R ) D. ( frac{4}{9} R ) | 11 |

1001 | The angular momentum of the earth revolving round the sun, is proportional to ( r^{n}, ) where ( r ) is the distance between the centres of earth and the sun. The value of ( n ) is : A . 1 B. -2 c. -1 D. ( frac{1}{2} ) | 11 |

1002 | Gravitational force can be repulsive. A. True B. False | 9 |

1003 | A geo-stationary satellite is orbiting around earth at height of ( 30,000 mathrm{km} ) in circular orbit. The radius of the earth is taken as ( 6000 mathrm{km} . ) The geo-stationary satellite comes back to its position after one revolution in exactly 24 hours. Let the acceleration due to gravity ( (g) ) ( 10 m / s^{2} ) and mass of satellite be 1000 kg; calculate the work done in 12 hours when moving under gravitational force. A ( left..3 .6 pi times 10^{14}rightrfloor ) В ( cdot 2 pi times 7.2 pi times 10^{14} ) C ( .1 .8 pi times 10^{14} mathrm{J} ) D. 0 | 11 |

1004 | Read the assertion and reason carefully to mark the correct option out of the options given below: Assertion: When radius of orbit of a satellite is made 4 times, its time period becomes 8 times. Reason : Greater the height above the surface of earth, greater is the time period of revolution. A. If both assertion and reason are true and the reason is the correct explanation of the assertion B. If both assertion and reason are true but reason is not the correct explanation of the assertion c. If assertion is true but reason is false D. If assertion is false but reason is true | 11 |

1005 | A particle is kept at rest at a distance ( boldsymbol{R} ) (earth’s radius) above the earth’s surface. The minimum speed with which it should be projected so that it does not return is A ( cdot sqrt{frac{G M}{4 R}} ) в. ( sqrt{frac{G M}{2 R}} ) c. ( sqrt{frac{G M}{R}} ) D. ( sqrt{frac{2 G M}{4 R}} ) | 11 |

1006 | A solld sphere of radıus ( r ) Is tloating at the interfare of two immiscible liquids of densities ( p_{1} ) and ( p_{2}left(p_{2}>p_{1}right), ) half of its volume lying in each. The height of the upper liquid column from the interfare of the two liquids is ( h . ) The force exerted on the upper liquid is (atmosphere pressure ( =p_{o} ) and acceleration due to gravity is ( g ) ): ( ^{mathbf{A}} cdot p_{0} pi r^{2}+left(h-frac{2}{3 r}right) pi r^{2} p_{1} g ) B. ( left(h-frac{2}{3 r}right) pi r^{2} p_{1} g ) c. ( frac{2}{3} pi r^{3} p_{1} g ) ( mathbf{D} cdot P_{0} times pi r^{2} ) | 11 |

1007 | A body of weight ( 72 mathrm{N} ) moves from the surfaceof earth at a height half of the radius of theearth, then gravitational force exerted on it will be : A. 36 N в. 32 N c. 144 N D. 50 N | 11 |

1008 | The escape velocity for a body projected vertically upwards from the surface of earth is ( 11 mathrm{km} / mathrm{s} ). If the body is projected at an angle of ( 45^{0} ) with the vertical, the escape velocity will be A. ( 11 sqrt{2 mathrm{km} / mathrm{s}} ) . B. 22 km/s c. ( 11 mathrm{km} / mathrm{s} ) D. ( 11 / sqrt{2 mathrm{m}} / mathrm{s} ) | 11 |

1009 | At perihelion, the gravitational potential energy of Pluto in its orbit has A. its maximum value B. its mimimum value c. the same value as at every other point in the orbitt D. value which depends on sense of rotation | 11 |

1010 | whose hemispherical base is of diameter ( 0.20 mathrm{m} . ) The height of the flask is ( 0.25 mathrm{m} ). The flask is filled to the brim with 2.5 litres ( left(1 text { litre }=10^{-3} m^{3}right) ) of water and sealed with a glass lid. What is the approximate magnitude of the total vertical force exerted by the water on the curved surface of the flask? (Take the acceleration due to gravity, ( g, ) to be ( 10 m s^{-2} ) ). ( A cdot O N ) B. 78.5 c. 53.5 N D. 25.0 | 11 |

1011 | In the relation ( F=frac{G M m}{r^{2}}, ) the quantity ( G ) A. depends on the value of ( g ) at the place of observation. B. is used only when the earth is one of the two masses. C. is greatest at the surface of the earth D. is universal constant in nature. | 11 |

1012 | There are ( _{–} ) gravitational lines of force inside a spherically symmetric shell A. Infinitely many B. Zero c. varying number depending upon surface area D. Varying number depending upon volume | 11 |

1013 | The gravitational force between two particles is ( F, ) if the objects are stationary and separated by a distance of ( 1 mathrm{m} ). If the objects starts moving in opposite directions, from rest with uniform acceleration of ( a=1 m / s^{2} ) then the force between them after 3 secs will be A. 4 F/ 5 B. F/100 c. ( 4 F / 121 ) D. F/2 | 11 |

1014 | What is the gravitational potential energy? | 11 |

1015 | Mass of an object on moon will be A. One sixth of its value on earth B. Ten times it’s value on earth c. six times it’s value on earth D. Same as on earth | 9 |

1016 | The acceleration due to gravity is: A. more at the equator than at the poles B. not effected by the rotation of the earth C. affected by the rotation of the earth D. not effected by the latitude | 11 |

1017 | Calculate the distance from the surface of the earth at which the acceleration due to gravity is the same below and above the surface of the earth. | 11 |

1018 | The acceleration due to gravity at a place is ( 0.2 m / s 2 . ) Find its height above the earth’s surface. | 11 |

1019 | If a particle is slowly brought from reference point to another point ( boldsymbol{P} ) in a gravitational field, then work done per unit mass by the external agent is (at that point) A. gravitational force B. gravitational field intensity c. gravitation potential D. none of the above | 11 |

1020 | Q Type your question the surface of Mars it is ( 4.0 m s^{-2} . A 60 ) kg passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represents the weight (net gravitational force) of the passenger as a function of time.?? ( A ) B. B ( c cdot c ) ( D ) | 11 |

1021 | A particle of mass ( mathrm{M} ) is situated at the centre of spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be A. ( -frac{3 G M}{a} ) В. ( -frac{2 G M}{a} ) c. ( -frac{G M}{a} ) D. ( -frac{4 G M}{a} ) | 11 |

1022 | The kinetic energy needed to project a body of mass ( m ) from earth’s surface radius ( R ) ) to infinity is A ( cdot frac{m g R}{2} ) в. ( 2 m g R ) c. ( m g R ) D. ( frac{m g R}{4} ) | 11 |

1023 | An artificial satellite in the presence of frictional forces will move into an orbit closer to the earth and may have increased kinetic energy. Explain this. | 11 |

1024 | Find the binding energy of a body of mass ( 50 mathrm{kg} ) at rest on the surface of the earth. ( operatorname{given} G=6.67 times 10^{-11} N m^{2} / k g^{2} ) ( boldsymbol{R}=mathbf{6 4 0 0 k m}, boldsymbol{M}=mathbf{6} times mathbf{1 0}^{mathbf{2 4}} boldsymbol{k g} ) | 11 |

1025 | If suddenly the gravitational force of attraction between earth and a satellite revolving aroung it becomes zero, then the satellite will A. continue to move in its orbit with same velocity B. Move tangentialy to the original orbit with the same velocity c. Become satationary in its orbit D. Move towards the earth | 9 |

1026 | Two particles of masses ( m_{1} ) and ( m_{2} ) initially at rest at infinite distance from each other, move under the action of mutual gravitational pull. Show that at any instant their relative velocity of approach is ( sqrt{2 Gleft(m_{1}+m_{2}right) / R, text { where }} ) ( mathrm{R} ) is their separation at that instant. | 11 |

1027 | The maximum and minimum distance of earth from sun are ( r_{1} ) and ( r_{2} ) respectively What will be the distance of earth from sun when its position vector is perpendicular to the major axis of its orbit A ( cdot frac{r_{1}+r_{2}}{4} ) в. ( left(frac{r_{1}+r_{2}}{r_{1}-r_{2}}right) ) c. ( frac{2 r_{1} r_{2}}{r_{1}+r_{2}} ) D. ( frac{r_{1}+r_{2}}{3} ) | 11 |

1028 | The kinetic energy needed to project a body of mass ( m ) from the earth surface (radius ( R ) ) to infinity is ( mathbf{A} cdot m g R / 2 ) в. ( 2 m g R ) ( c . m g R ) D. ( m g R / 4 ) | 11 |

1029 | A satellite of mass m revolves around the earth of radius ( R ) at a height ( x ) from its surface. If ( g ) is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is ( mathbf{A} cdot g x ) B. ( sqrt{frac{g R^{2}}{R+x}} ) c. ( frac{g R^{2}}{R+x} ) D. ( frac{g R}{R-x} ) | 11 |

1030 | If the earth stops rotating about its axis, then the magnitude of gravity A. increases everywhere on the surface of earth B. will increase only at the poles c. will not change at the poles D. All of the above | 11 |

1031 | A planet of mass ( m ) is moving in an elliptical orbit round the sun of mass ( M . ) If the maximum and minimum distances of the planet from the sun be ( l_{1} ) and ( l_{2}, ) the angular momentum of the planet about the sun will be A ( cdot m frac{G M m}{sqrt{left(l_{1}+l_{2}right)}} ) в. ( m sqrt{frac{l_{1}+l_{2}}{G M l_{1} l_{2}}} ) c. ( m sqrt{frac{2 G M l_{1} l_{2}}{left(l_{1}+l_{2}right)}} ) ( D ) | 11 |

1032 | Two stationary particles of masses ( mathbf{M}_{1} ) and ( mathrm{M}_{2} ) are at distance d apart. A third particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from ( mathbf{M}_{mathbf{1}} ) is ( ^{mathrm{A}} cdot mathrm{d}left(frac{sqrt{mathrm{M}_{2}}}{sqrt{mathrm{M}_{1}}-sqrt{mathrm{M}_{2}}}right) ) В. ( mathrm{d}left(frac{sqrt{mathrm{M}_{1}}}{sqrt{mathrm{M}_{1}}+sqrt{mathrm{M}_{2}}}right) ) ( ^{mathrm{c}} cdot mathrm{d}left(frac{sqrt{mathrm{M}_{1}}}{sqrt{mathrm{M}_{1}}-sqrt{mathrm{M}_{2}}}right) ) D. ( mathrm{d}left(frac{mathrm{M}_{1}}{mathrm{M}_{1}+mathrm{M}_{2}}right) ) | 11 |

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