Gravitation PYQs Set 2 (PDF)

Set 2 of 12 · Questions 31-60 of 331

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Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 2 (Q31-60)
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31. $The value of acceleration due to gravity at a depth ' d' from the surface of earth and at an altitude ' h' from the surface of earth are in the ratio$ (1) $1 : 1$ (2) $\frac{R - 2 h}{R - d}$ (3) $\frac{R - d}{R - 2 h}$ (4) $\frac{R - d}{R - h}$ 32. $The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:$ (1) $\frac{v}{3}$ (2) $\frac{v}{4}$ (3) $\frac{v}{12}$ (4) $\frac{v}{6}$ 33. $The gravitational potential at a point above the surface of earth is - 5.12 \times 10^{7} J / kg and the acceleration due to gravity at that point is 6.4 m / s^{2} . Assume that the mean radius of earth to be 6400 km . The height of this point above the earth's surface is:$ (1) $1600 km$ (2) $540 km$ (3) $1200 km$ (4) $1000 km$ 34. $The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is:$ (1) $\frac{3}{2} m g R$ (2) $mgR$ (3) $2 mgR$ (4) $\frac{1}{2} m g R$ 35. $The height at which the acceleration due to gravity becomes \frac{g}{9} (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is$ (1) $\frac{R}{2}$ (2) $\frac{R}{2}$ (3) $2 R$ (4) $2R$ 36. $A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be:$ (1) $\frac{2}{3} m g R$ (2) $3mgR$ (3) $\frac{1}{3} m g R$ (4) $mg2R$ 37. $The kinetic energy of a revolving satellite (mass m) at a height equal to thrice the radius of the earth (R) is$ (1) $\frac{mgR}{8}$ (2) $\frac{mgR}{16}$ (3) $\frac{mgR}{2}$ (4) $\frac{mgR}{4}$ 38. $A ball is dropped from a spacecraft revolving around the earth at a height of 120 km. What will happen to the ball?$ (1) $it will fall down to the earth gradually$ (2) $it will go very far in the space$ (3) $it will continue to move with the same speed along the original orbit of spacecraft$ (4) $it will move with the same speed, tangentially to the spacecraft.$ 39. $Escape velocity of a body from earth is 11.2 km / s . If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:$ (1) $11.2 km / s$ (2) $8.4 km / s$ (3) $\frac{4.2 km}{s}$ (4) $7.9 km / s$ 40. $A body is thrown from the surface of the earth with velocity ' u' m / s . The maximum height in m above the surface of the earth upto which it will reach is (R = radius of earth, g = acceleration due to gravity)$ (1) $\frac{u ^{2} R}{2 gR - u ^{2}}$ (2) $\frac{2 u ^{2} R}{gR - u ^{2}}$ (3) $\frac{u ^{2} R ^{2}}{2 g R ^{2} - u ^{2}}$ (4) $\frac{u ^{2} R}{gR - u ^{2}}$ 41. $The minimum and maximum distances of a planet revolving around the Sun are x_{1} and x_{2} . If the minimum speed of the planet on its trajectory is v_{0} then its maximum speed will be:$ (1) $\frac{v _{0} x _{1}^{2}}{x _{2}^{2}}$ (2) $\frac{V _{0} x _{2}^{2}}{x _{1}^{2}}$ (3) $\frac{v _{0} x _{1}}{x _{2}}$ (4) $\frac{v _{0} x _{2}}{x _{1}}$ 42. $Suppose the charge of a proton and an electron differ slightly. One of them is - e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen m_{h} = 1.67 \times 1 0^{-27} kg]$ (1) $1 0^{-20} C$ (2) $1 0^{-23} C$ (3) $1 0^{-37} C$ (4) $1 0^{-47} C$ 43. $Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g^{'}, then$ (1) $g^{'} = g /9$ (2) $g^{'} = 27 g$ (3) $g^{'} = 9 g$ (4) $g^{'} = 3 g .$ 44. $The value of acceleration due to gravity at a height of 10 km from the surface of earth is x . At what depth inside the earth is the value of the acceleration due to gravity has the same value x ?$ (1) $10 km$ (2) $15 km$ (3) $5 km$ (4) $20 km$ 45. $A rocket is launched straight up from the surface of the earth. When its altitude is \frac{1}{3} of the radius of the earth, its fuel runs out and therefore it coasts. If the rocket has to escape from the gravitational pull of the earth, the minimum velocity with which it should coast is (Escape velocity on the surface of the earth is 11.2 kms^{- 1} .)$ (1) $11.2 kms^{- 1}$ (2) $10.7 kms^{- 1}$ (3) $9.7 kms^{- 1}$ (4) $8.7 kms^{- 1}$ 46. $A body of mass m is raised to a height 10 R from the surface of earth, where R is the radius of earth. The increase in potential energy is (G = universal constant of gravitation, M = mass of earth and g = acceleration due to gravity)$ (1) $\frac{GMm}{11 R}$ (2) $\frac{GMm}{10 R}$ (3) $\frac{mgR}{11 G}$ (4) $\frac{10 GMm}{11 R}$ 47. $For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is$ (1) $1/2$ (2) $1/ 2$ (3) $2$ (4) $2$ 48. $A satellite is revolving in a circular orbit at a height ' h' above the surface of the earth of radius ' R'. The speed of the satellite in its orbit is one-fourth. The escape velocity from the surface of the earth. The relation between ' h' and ' R' is$ (1) $h = 2 R$ (2) $h = 3 R$ (3) $h = 5 R$ (4) $h = 7 R$ 49. $The escape velocity from a spherical planet A is 10 km / s . The escape velocity from another planet B whose density and radius are 10 % of those of planet A, is____m / s .$ (1) $1000$ (2) $10002$ (3) $2005$ (4) $10010$ 50. $Calculate angular velocity of earth so that acceleration due to gravity at 60^{\circ} latitude becomes zero. (Radius of earth = 6400 km, gravitational acceleration at poles = 10 m / s^{2}, cos 60^{\circ} = 0.5)$ (1) $7.8 \times 10^{- 2} rad / s$ (2) $0.5 \times 10^{- 3} rad / s$ (3) $1 \times 10^{- 3} rad / s$ (4) $2.5 \times 10^{- 3} rad / s$ 51. $A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms^{- 2} at the north pole and the radius of the earth = 6400 k m)$ (1) $194.32 N$ (2) $194.66 N$ (3) $195.32 N$ (4) $195.66 N$ 52. $Dependence of intensity of gravitational field (E) of earth with distance (r) from center of earth is correctly represented by:$ (1) (2) (3) (4) 53. $The distance of two planets from the sun are 1 0^{13} m and 1 0^{12} m respectively. The ratio of time periods of the planets is$ (1) $10$ (2) $1010$ (3) $10$ (4) $1/ 10$ 54. $If the distance of the earth from Sun is 1.5 x 1 0^{6} km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:$ (1) $6x 1 0^{7} km$ (2) $6 x 1 0^{6} km$ (3) $3x 1 0^{6} km$ (4) $3x 1 0^{7} km$ 55. $An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of earth. Which of the following could explain this?$ (1) $Both the mass and radius of the planet are half as that of earth.$ (2) $Radius of the planet is half as that of earth, but the mass is the same as that of earth.$ (3) $Both the mass and radius of the planet are twice as that of earth.$ (4) $Mass of the planet is half as that of earth, but radius is same as that of earth.$ 56. $The gravitational potential energy of a system of three masses m, 2 m and 3 m placed at three vertices of equilateral triangle of side ' a' is$ (1) $- 11 \frac{Gm}{a}$ (2) $- 11 \frac{G m ^{2}}{a ^{2}}$ (3) $- 11 \frac{G m ^{2}}{a}$ (4) $- 11 \frac{Gm}{a ^{2}}$ 57. $If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?$ (1) $Raindrops will fall faster.$ (2) $Walking on the ground would become more difficult.$ (3) $Time period of a simple pendulum on the$ (4) $g on the Earth will not change.$ 58. $The ratio of orbital velocity of a body near to the surface of a planet and escape velocity of a body from the surface of the same planet is$ (1) $2 : 1$ (2) $5 : 1$ (3) $1 : 2$ (4) $1 : 5$ 59. $If the mass of a body is M on the surface of the earth, the mass of the same body on the surface of the moon is$ (1) $M$ (2) $zero$ (3) $M /6$ (4) $6 M$ 60. $A planet is moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the sun (i) is zero in no part of the motion. (ii) is zero in some parts of the orbit. (iii) is zero in one complete revolution. (iv) is zero in any small part of the orbit. Which of the following is true?$ (1) $Only (iii) is true$ (2) $(ii), (iii) and (iv) are true$ (3) $(ii) and (iii) are true$ (4) $Only (i) is true$