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Gravitation, , Gravitational force, field & acceleration (Level0), , If the radius of the earth is 6.4 x 106 m, the weight of a, 100 kg body, if taken to a height of 3.6 x 106 m above, sea level, will be, (a) 72 kg wt, (b) 60 kg wt, (c) 54 kg wt, (d) 41 kg wt, 3. The value of acceleration due to gravity at the bottom, of a sea 30 km deep is, (a) 9.34 rn/s2(b) 9.07 m/s2(c) 9.14 rn/s2 (d) 9.76 m/s2, 4. ge and gp denote the acceleration due to gravity on the, surface of the earth and another planet whose mass and, radius are twice that of the earth. The relation that, holds true is, 2., , (a) gp=, , g, 2, 1, ge, g e (b) gp= e (c) gp=2 ge (d) gp=, 3, 2, 2, , 5., , 1., , The mass of the electron is 9 x 10-31kg. If the two, electrons are separated by a distance of 1m, the, Gravitational force of attraction between them is, (a) 5.40 x 10-51 N, (b) 5.40 x 10-44 N, -42, (c) 5.40 X 10 N, (d) 5.40 x 10-71 N, , 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, (b) increase, (c) remain unchanged, (d) become zero, 6. If the radius of the earth shrinks by 1 %, its mass, remaining same, the acceleration due to gravity on the, surface of the earth will, (a) decrease by 2%, (b) decrease by 0.5%, (c) increase by 2%, (d) increase by 0.5%, 7. The height above the surface of the earth where, acceleration due to gravity is 1/64 of its value at the, surface of the earth is, (a) 45 x 106 m, (b) 45 x 103 m, 5, (c) 54 x 10 m, (d) 54 x 107 m, 8. At the earth's surface, a freely suspended object is, struck a horizontal blow with a hammer. The object is, taken to the moon, suspended freely and struck an, equally strong blow with the same hammer. The, horizontal speed resulting on the moon will be, (a) equal to that on the earth, (b) half that on the earth, (c) five times that on the earth, Page 2
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(d) one-fifth that on the earth, 9. Three uniform spheres of mass M and radius R each, are kept in such a way that each touches the other two., The magnitude of the gravitational force on any of the, spheres due to other two is, 3 GM , 3 GM , 3 GM , 3GM , (a), (b), (c), (d), 4 R2, 4 R2, 2 R2, R2, 10. Take the effect of bulging of earth and its rotation in, account. Consider the following statements, (A) there are points outside the earth where the, value of g is equal to its value at the equator, (B) there are points outside the earth where the, value of g is equal to its value at the poles, (a) Both A and B are correct, (b) A is correct but B is wrong, (c) B is correct but A is wrong, (d) Both A and B are wrong, 11. In an experiment for determining the gravitational, acceleration g of a place with the help of a simple, pendulum, the measured time period square is plotted, against the string length of the pendulum in the figure., What is the value of g at the place?, , (a) Zero, (b) g/2, (c) g, (d) 3g/4, 18. A body is suspended from a spring balance kept in a, satellite. The reading of the balance is W1 when the, satellite goes in an orbit of radius R and is W2 when it, goes in an orbit of radius 2R, (a) W1 = W2, (b) W1 < W2, (c) W1 > W2, (d) W1W2, 19. The variation of acceleration due to gravity g with, distance d from centre of the earth is best represented, by (R = Earth’s radius):, (a), (b), , (c), , (d), , LEVEL – 1, 20. Infinite number of masses, each of mass m, are placed, along a straight line at distances r, 2r, 4r, 8r, etc from a, reference point O. The gravitational field intensity at, point O will be, (a) 9.81 m/s2 (b) 9.87 m/s2 (c) 9.91 m/s2 (d) 10.0 m/s2, 12. The change in the value of acceleration of earth, towards sun, when the moon comes from the position, of solar eclipse to the position on the other side of earth, in line with sun is (mass of the moon = 7.36 x 1022 kg,, radius of the moon’s orbit = 3.8 x 108 m)., (a) 673 105 m / s 2, (b) 673 103 m / s 2, (c) 673 102 m / s 2, (d) 673 103 m / s 2, 13., choose the one that best describes the two statements, 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, 14. 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 earth. When both ‘d’ and ‘h’ are much, smaller than the radius of earth, then which one of the, following is correct?, (a) d , , h, 2, , (b) d , , 3h, 2, , (c) d = 2h, , (d) d = h, , 15. A high jumper can jump 2.0m 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) 4m (b) 8m, (c) 24m (d) 12m, 16. At what height from the surface of the earth, the value, of g will be reduced to 64% of its value at the surface, of the earth? (Radius of the earth = 6,400 km), (a) 6400km (b) 1600km (c) 5000km (d) 1000km, 17. Gravitational acceleration at the centre of earth is, , (a), , 5Gm, 3Gm, (b), 2, 2r 2, 4r, , (c), , 4Gm, 3r 2, , (d), , Gm, r, , 21. A mass m is divided into two parts xm and (1 –x). For, a given separation, the value of x for which the, gravitational attraction between the two pieces, becomes maximum is, (a), , 1, 2, , (b), , 3, 5, , (c) 1, , (d) 0, , 22. A spherical shell is cut into two pieces along a chord, as shown. For point P and Q, P, , Q, , (a) IP > IQ (b) IP < IQ, (c) IP = IQ (d) IP = IQ, 0, 23. A spherical planet far out in space has a mass M0 and, diameter D0. A particle of mass m falling freely near, the surface of this planet will experience an, acceleration due to gravity which is equal to, , GM 0, D02, 4GM 0, (c), D02, (a), , 4mGM 0, D02, GmM 0, (d), D02, (b), , 24. What is the value of acceleration at a height equal to, the radius of earth?, (a) g/2, (b) g/4 (c) 3g/4 (d) 0, 25. If the acceleration due to gravity at earth is ‘g’ and, mass of earth is 80 times that of moon and radius of, earth is 4 times that of moon, the value of ‘g’ at the, surface of moon will be, (a) g, (b) g/20, (c) g/5, (d) 320g, Page 3
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26. If the change in the value of ‘g’ at a height h above the, surface of the earth is the same as at a depth x below it,, when both x and h are much smaller than the radius of, the earth, then, (a) x = h (b) x = 2h (c) x = h/2, (d) x = h2, 27. From a sphere of mass M and radius R a smaller sphere, of radius R/2 is curved out such that the cavity made in, a original sphere is between its centre and the, periphery., (see figure). For the configuration in the figure where, the distance between the centre of the original sphere, and the removed sphere is 3R, the gravitational force, between the two sphere is, , (a), , 41GM 2, 450 R 2, , 2, 2, (b) GM (c) 41GM, , 225R 2, , 3600 R 2, , 2, (d) 59GM, , 450 R 2, , 28. The gravitational field due to the left over part of a, uniform sphere (from which a part as. (shown, has been, removed out), at a very far off point P, located as, shown would be (nearly):, , (a), , 5 GM, (b) 8 GM, (c) 7 GM, 2, 2, 6 x, 9 x, 8 x2, , Gravitational potential & potential, energy, , (d) 6 GM, 2, 7 x, , 29. A particle on earth’s surface is given a velocity equal, to its escape velocity. Its total mechanical energy will, be, (a) negative, (b) positive (c) zero, (d) infinite, 30. When escape velocity is given to a particle on surface, of earth, its total energy is, (a) zero, (b) greater than zero, (d) -, , (c) less than zero, , GMm, 2R, , 31. The gravitational field in a region is given by:, , , ^, , ^, , E (5 N / kg ) i (12 N / kg ) j, , If the potential at the origin is taken to be zero then the, ratio of the potential at the points (12m, 0) and (0, 5m), is:, (a) zero, (b) 1 (c) 144/25, (d) 25/144, 32. Two bodies of masses m and 4m are placed at a, distance r. The gravitational potential at a point on the, line joining them where the gravitational field is zero, is:, 4Gm, (a) , (b) 6Gm, r, r, 9Gm, (c) , (d) zero, r, , 33. A particle of mass 10g is kept on the surface of a, uniform sphere of mass 100kg and radius 10 cm. Find, the work to be done against the gravitational force, between them to take the particle for away from the, sphere (you may take G = 6.67 x 10-11 Nm2/kg2), (a) 13.34 1010 J, (b) 3.33 1010 J, (c) 6.67 109 J, (d) 6.67 1010 J, 34. The gravitational field due to a mass distribution is, , Page 4
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E=, , A, in x-direction. Here A is a constant. Taking, x2, , the gravitational potential to be zero at infinity,, potential at x is, 2A, A, 2A, A, (a), (b) 3, (c), (d), x, x, x, 2x 2, 35. The kinetic energy needed to project a body of mass m, from the earth’s surface to infinity is, (a) ¼ mgR, (b) ½ mgR (c) mgR, (d) 2 mgR, 36. A particle is kept at rest at a distance 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, 2GM, GM, GM, GM, (a), (b), (c), (d), R, 4R, 2R, R, 37. A ring has a total time mass m but non-uniformly, distributed over its circumference. The radius of the, string is R. A point mass m is placed at the centre of, the ring. Work done in taking away this point mass, from centre of a infinity is, GMm, GMm, (a) , (b), R, R, GMm, (c), (d) cannot be predicted, 2R, 38. A person varying a mass of 2 kg from A to B. The, increase in kinetic energy of the mass is 4 J and the, work done by the person on the mass is 10 J. The, potential difference between B and A is, (i.e. VB VA), (a) 4 J/kg (b) 7 J/kg (c) 3 J/kg, (d) 7 J/kg, 39. A person brings a mass of 1 Kg from infinity to a point, A. Infinity the mass was at rest but it moves at a speed, of 2 m/s as it reaches A. The work done by the person, on the mass is 3 J. The potential at A is, (a) 3 J/kg (b) 2 J/kg (c) 5 J/kg (d) none of these, 40. The gravitational field in a region is given by, , , ^, , ^, , g 5N / kg i 12 N / kg j . The change in the, , gravitational potential energy of a particle of mass 2kg, when it is taken from the origin to a point (7m, -3m) is:, (a) 71J, , (b) 13, , 58 J, , (c) -71J, , (d) 2J, , 41. Four particles, each of mass M and equidistant from, each other, move along a circle of radius R under the, action of their mutual gravitational attraction. The, speed of each particle is:, (a), (c), , GM, (1 2 2), R, , (b) 1 GM (1 2 2), , GM, R, , (d), , 2, , R, GM, 2 2, R, , 42. If g is the acceleration due to gravity on the earth’s, surface, the gain in the potential energy of object of, mass m raised from the surface of the earth to a height, equal to the radius R of the earth is, , 1, 1, (a) 2 mgR (b), mgR (c) 4 mgR, 2, , 43. A particle of mass M is placed a at the centre of a, uniform spherical shell of mass 2 M and radius R., The gravitational potential on the surface of the shell is, GM, 3GM, 2GM, (a) , (b) , (c) , (d) zero, R, R, R, 44. Two starts, each of mass m and radius R are, approaching each other for a head – on collision. They, start approaching each other when their separation is r,, r >> R. If their speeds at this separation are negligible,, the speed with which they collide would be, , 1 1, , 2r r , , 1 1, , R r, , (b) v Gm , , 1 1, , R r, , (d) v Gm , , (a) v = Gm , , 1 1, , 2R r , , (c) v Gm , , 45. A body of mass m is raised to a height h above the, surface of the earth of mass M and radius R until its, gravitational potential energy increases by, , 1, mgR ., 3, , The value of h is, (a), , R, 3, , (b), , R, 2, , mR, mR, (d), M, M m, , (c), , 46. A body of mass m is moved to a height equal to the, radius of the earth R. The increase in its PE is, (a) mgR, (b) 2mgR, (c), , 1, mgR, 2, , (d), , mgR, 2, , 47. For a uniform ring of mass ‘M’ and radius R at its, centre, (a) Field and potential both are zero, , GM, R, GM, (c) Field is zero but potential is R, GM, GM, (d) Magnitude of field is, and potential is 2, R, R, (b) Field is zero but potential is, , 48. A body, which is initially at rest at a height R above, the surface of the earth of radius R, falls freely towards, the earth, then its velocity on reaching the surface of, the earth is, (a), , 2gR, , (c), , 3, gR, 2, , (b), , gR, , (d), , 4gR, , 49. What is the work done in placing three identical, particles each of mass m at the vertices of an, equilateral triangle of side L?, , 3Gm2, L, -Gm 2, (c), L, (a) +, , 3Gm 2, L, Gm 2, (d), L, (b) -, , 50. ve and vp denotes the escape velocity from the earth, and another planet having twice the radius and the, same mean density as the earth. Then, , (d) mgR, Page 5
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(b) ve =, , (a) re = vp, (c) v e =2v p, , vp, 2, , (d) ve =, , vp, 4, , 51. Two hypothetical planets of masses m1 and m2 are at, rest when they are infinite distance apart. Because of, the gravitational force they move towards each other, along the line joining their centres. What is their speed, when their separation is ‘d’? (Speed of m1 is v1 and that, of m2 is v2), , (a) v1 v2, (b) v m, 1, 2, , 2G, 2G, , v2 m1, d (m1 m2 ), d (m1 m2 ), , (c) v m, 1, 1, , 2G, 2G, , v2 m2, d (m1 m2 ), d (m1 m2 ), , (c) v m 2G , v m 2G, 1, 2, 2, 1, m1, , m2, , 52. Two stationary masses m1 and m2 are separated by, infinite distance. They ineract only gravitationally., Calculate their velocity of approach at a distance r from, each other., 1/2, , 2Gm1 , (a) , , m1 m2 , , 2G (m1 m2 ) , , r, , , 1/2, , (b) , , 2G m2 , (c) , , m1 m2 , , 1/2, , (d) [2Gr ]1/2, , 57. 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 R equal to, the radius of the earth is, (a) ½ mgR (b) 2mgR, (c) mgR, (d) ¼ mgR, Planet & satellite, , Level – 0, 53. An artificial satellite moving in a circular orbit around, the earth has a total (kinetic + potential) energy E0. Its, potential energy is, (a) -E0, (b) 1.5E0, (c) 2E0, (d) E0, 54. Figure shows the elliptical path of a planet about the, sun. The two shaded, c, parts have equal area. If, b, t1 and t2 be the time, taken by the planet to go, S, a, d, from a to b and from c, to d respectively, (a) t1 < t2, (b) t1 = t2, (c) t1 > t2, (d) insufficient information to deduce the relation, between t1 and t2., 55. 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, (b) 129, (c) 182.5, (d) 730, 56. 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., 57. A comet is revolving around the sun in a highly, elliptical orbit. Which of the following will remain, constant throughout its orbit?, (a) Kinetic energy (b) Potential energy, (c) Total energy, (d) Angular momentum, 58. The orbital velocities of a body close to the earth’s, surface is, (a) 8km/s, (b) 11.2 km/s, (c) 3 x 108 m/s, (d) 2.2 x 103 km/s, 59. The planet mercury is revolving in an elliptical orbit, around Sun as shown. The kinetic energy of mercury, will be greatest at, , Page 6
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B, , C, , D, , Sun, A, E, , (a) A, (b) B (c) C (d) D (e) E, 60. Two satellites A and B go round a planet in circular, orbits having radii 4R and R respectively. If the speed, of satellite A is 3V, the speed of satellite will be, (a) 12V, (b) 6V, (c) 4V/3, (d) 3V/2, 61. The speed of a planet moving around the sun in an, elliptical orbit is, (a) Lowest at the apogee, (b) Highest at the apogee, (c) Lowest at the perigee (d) none, 62. The linear velocity of a satellite in a circular orbit of a, given radius is, (a) proportional to its mass, (b) independent of its mass, (c) proportional to the square root of its mass, (d) inversely proportional to its mass, 63. The ratio of distance of two satellites from the centre, of earth is 1 : 4. The ratio of their time period of, rotation will be, (a) 1 : 4, (b) 4 : 1, (c) 1 : 8 (d) 8 : 1, 64. The radius of the planet Jupiter is 74,000 km. A, satellite completes a circular orbit around it once in, every 16.7 days. The radius of the orbit of the satellite, is 27 times the. radius of Jupiter. The mass of Jupiter is, (a) 2.3 x 1042 kg, (b) 2.3 x 1027 kg, 30, (c) 2.3 x 10 kg, (d) 2.3 x 1032 kg, 65. The period of revolution of an earth satellite close to, surface of earth is 90 minutes. The time period of, another satellite in an orbit at a distance of three times, the radius of earth from its surface will be, (a) 90 8 min, v2, (b) 360 min (c), 720 min (d) 270, r1, r2, min, P, Q, 66. A planet is, moving in an, v1, elliptical path, around the sun as shown in the figure. Speed of planet, in positions P and Q are v1 and v2 respectively with SP, = r1 and SQ = r2, then v1/v2 is equal to, 2, , r , r, r, (a) 1, (b) 2, (c) constant, (d) 1 , r2, r1, r2 , 67. 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, 68. The magnitude of gravitational potential energy of the, moon-earth system is U with zero potential at infinite, separation. The kinetic energy of the moon with respect, to the earth is K., (a) U < K, (b) U > K, (c) U = K, 69. The magnitude of gravitational potential energy of the, earth-satellite system is U with zero potential energy at, , infinite separation. The kinetic energy of satellite is K., Mass of satellite « mass of earth. Then, (a) K= 2U (b) K = U/2 (c) K = U, (d) K=4U, 70. If a satellite be rotating about a planet, which of the, following is true?, [U = Potential energy of planet satellite system, K =, kinetic energy of satellite, T = Total Mechanical, energy], (a) |U| = k = |T|, (b) k = |T| = |2U|, (c) 2k = |T| = |U|, (d) k = |T| = |1/2U|, 71. A planet of mass m is moving about the sun of mass M, in a circular orbit of radius R. Assuming the sun to be, at rest in an inertial reference frame, the total energy of, the planet-sun system is, (a) G mM (b) G mM (c) G mM (d) G mM, R, , R, , 2R, , 2R, , 72. 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 kms-1, the escape velocity from the surface of the, planet would be, (a) 1.1 kms -1, (b) 11 kms-1, -1, (c) 110 kms, (d) 0.11 kms-1, 73. If the angular velocity of a planet about its own axis is, halved, the distance of geostationary satellite of this, planet from the centre of the planet will become, (a) (2)1/3 times, (b) (2)3/2 times, 2/3, (c) (2) times, (d) 4 times, 74. The angular momentum (L) of earth revolving round, the sun is proportional to rn. Where r is the orbital, radius of the earth. The value of n is (assume the orbit, to be circular), (a) ½, (b) 1, (c) ½, (d) 2, LEVEL – 1, 75. The radius of a planet is R. A satellite revolves around, it in a circle of radius r with angular speed . The, acceleration due to gravity on planet’s surface will be, , r, r 3, r 23, r 2 2, (b), (c), (d), R, R, R, R2, 76. 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 2R?, (a) 2GmM, (b) GmM, 3, , 2, , (a), , (c), , 3R, GmM, 3R, , (d), , 2R, 5GmM, 6R, , 77. 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. Which of the following, statement is correct?, (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 remaining, constant., (d) The linear momentum of S remains constant in, magnitude., , Page 7
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78. In a satellite is the time of revolution is T. Then K.E. is, proportional to, (a), , 1, T 2/3, , (b), , 1, T, , (c), , 1, T2, , (d), , 1, T3, , 79. 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, , (b), , 2R, , (c) 2R, , (d) R, 2, , 80. The time period of a satellite of earth is 5 hours. If the, separation between the earth and the satellite is, increased to 4 times the previous value, the new time, period will become, (a) 10 hours, (b) 80 hours, (c) 40 hours, (d) 20 hours, 81. The escape velocity for a body projected vertically, upwards from the surface of earth is 11 km/s. If the, body is projected at an angle of 450 with the vertical,, the escape velocity will be, (a) 11 2km / s, (b) 22 km/s, (c) 11 km/s, (d) 11/ 2m / s, 82. 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 more with the same velocity in the, same orbit, (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, 83. 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) m1, (c) m0, (d) m1/2, 84. A planet has twice the density of earth but the, acceleration due to gravity on its surface is exactly the, same as on the surface of earth. Its radius in terms of, radius of earth R will be:, (a) R/4, (b) R/2, (c) R/3, (d) R/8, 85. The escape velocity for a planet is ve. A particle is, projected from its surface with a speed v for this, particle to move as a satellite around the planet,, (a), , ve, < v < ve, 2, , (b), , ve, < v < ve, 2, , (c) None of the above, 86. The escape velocity for a planet is ve. A particle,, initially at rest reaches the planet from a large distance, and passes through a tunnel through its centre. Its speed, at the centre of planet will be, (a) ve, (b) 1.5 ve, (c) 1.5ve, (d) 2ve, 87. If a small part separates from an orbiting satellite, the, part separated will, (a) fall to the earth directly, (b) move in a spiral path and finally reach the earth, (c) continue to move in the same orbit as the satellite, (d) move farther away from the earth gradually, , 88. A satellite is moving around the earth with velocity v., To make the satellite escape, the minimum percentage, increase in its velocity is nearly., (a) 41.4%, (b) 82.8%, (c) 100%, (d) None of these, 89. A satellite is revolving in a circular orbit at a height ‘h’, from the earth’s surface (radius of earth R; h<<R). The, minimum increase in its orbital velocity required, so, that the satellite could escape from the earth’s, gravitational field, is close to: (Neglect the effect of, atmosphere), , gR, , (a), , gR / 2, , (b), , (c) gR ( 2 1) (d) 2gR, 90. 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) gx, gR 2, Rx, , (c), , gR, Rx, , (b), , 1/ 2, , 2, (d) gR , Rx, , , , , , 91. Suppose the gravitational force varies inversely as the, nth power of distance. Then the time period planet in, circular orbit of radius R around the sun will be, proportional to, n 1 , , , 2 , , R, , n 1 , , , 2 , , (b) R , , n2 , , , 2 , , n, , (c) R, (d) R, 92. An artificial satellite moving in circular orbit around, the earth has a total (kinetic + potential) energy E0. Its, PE is, (a) -E0, (b) 1.5E0, (c) 2E0 (d) E0, 93. A person sitting in a chair in a satellite feels weightless, because, (a) the earth does not attract the objects in a satellite, (b) the normal force by the chair on the person, balances the earth’s attraction, (c) the normal force is zero, (d) the person in satellite is not accelerated., 94. The ratio of the energy required to raise a satellite upto, a height h above the earth to that the kinetic energy of, the satellite into the orbit there is (R = radius of earth), (a) h:R, (b) R:2h, (c) 2h:R, (d) R:h, 95. Two particles of equal mass ‘m’ go around a circle of, radius R under the action of their mutual gravitation, attraction. The speed of each particle with respect to, their centre of mass is:, (a), , GM, 2R, , (b), , GM, R, , (c), , GM, 4R, , (d), , GM, 3R, , Page 8
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(Gravitation) from competitive exams, 96. Two spherical bodies of mass M and 5M and radii R, and 2R are released in free space with initial separation, between their centers equal to 12R. If they attract each, other due to gravitational force only, then the distance, covered by the smaller body before collision is, [NEET-2015], , (a) 2.5R (b) 4.5 R (c) 7.5 R, , (d) 1.5R, , 97. 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. Then, [NEET – 2015 Re], (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, 98. A remote – sensing satellite of earth revolves in a, circular orbit at a height of 0.25 x 106 m above the, surface of earth. If earth’s radius is 6.38 x 106 m, and g = 9.8 ms-2, then the orbital speed of the, satellite is, [NEET – 2016 Phase – I], (a) 6.67 km s-1 (b) 7.76 km s-1, (c) 8.56 km s-1 (d) 9.13 km s-1, 99. The ratio of escape velocity at earth (Ve) to the, escape velocity at a planet (vP) whose radius and, density are twice as that of earth is [NEET-2016, Phase-I], (a) 1: 2, (b) 1 : 2, (c) 1: 2 2, (d) 1 : 4, 100. The kinetic energies of a planet in an elliptical, orbit about the Sun, at positions A, B and C are, KA, KB and KC, respectively. AC is the major axis, and SB is perpendicular to AC at the position of, the Sun S as shown in the figure. Then, [NEET - 2018], , (a) K B K A KC, (c) K A K B KC, K B K A KC, , (b) K A K B KC, (d), , 101. A body weighs 200 N on the surface of the, earth. How much will it weigh half way down to, the centre of the earth?, [NEET – 2019], (a) 150 N, (b) 200 N, (c) 250 N, (d) 100 N, 102. 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:, [NEET - 2019], (a) mgR, (b) 2mgR, 1, 3, (c) mgR, (d) mgR, 2, 2, 103. The time period of a geostationary satellite is, 24 h, at a height 6RE (RE is radius of earth) from, surface of earth. The time period of another, satellite whose height is 2.5 RE from surface will, be [Odisha NEET 2019], 12, 24, h (d), h, (a) 6 2h (b) 12 2h (c), 2.5, 2.5, 104. Assuming that the gravitational potential, energy of an object at infinity is zero, the change, in potential energy (final – initial) of an object of, mass m, when taken to a height h from the surface, of earth (of radius R), is given by, [Odisha, NEET 2019], GMmh, GMm, GMm, (a) , (b), (c) mgh (d), Rh, Rh, R(R h), NTA Questions, 105., If the angular momentum of a planet of mass m,, moving around the Sun in a circular orbit is L, about, the center of the Sun, its areal velocity is: [JEE mains, 2019], , (a), , 4L, m, , (b), , L, m, , (c), , L, 2m, , (d), , 2L, m, , 106. Two satellites, A and B have masses m and, 2m respectively. A is in a circular orbit of radius, R, and B is in a circular orbit of radius 2R around, the earth. The ratio of their kinetic energies,, TA/TB, is:, 1, 1, (a) 2, (b), (c) 1, (d), 2, 2, 107. The energy required to take a satellite to a, height ‘h’ above Earth surface (radius of Earth =, 6.4 x 103 km) is E1 and kinetic energy required for, the satellite to be in a circular orbit at this height is, E2. The value of h for which E1 and E2 are equal,, is:, (a) 1.28 x 104 km, (b) 6.4 x 103 km, Page 9
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(c) 3.2 x 103 km, , (d) 1.6 x 103 km, , 108. A satellite is moving with a constant speed v, in circular orbit around the earth. An object of, mass ‘m’ is ejected from the satellite such that it, just escapes from the gravitational pull of the, earth. At the time of ejection, the kinetic energy of, the object is:, 3, (a) mv 2, (b) mv 2, 2, 1, (c) 2mv 2, (d) mv 2, 2, 109. Two stars of masses 3 x 1031 kg each, and at, distance 2 x 1011 m rotate in a plane about their, common centre of mass O. A meteorite passes, through O moving perpendicular to the star’s, rotation plane. In order to escape from the, gravitational field of this double star, the, minimum speed that meteorite should have at O, is:, (Take Gravitational constant G = 6.67 x 10-11 Nm2, kg-2), (a) 1.4 x 105 m/s (b) 24 x 104 m/s, (c) 3.8 x 104 m/s (d) 2.8 x 105 m/s, repeated, 110. A satellite is revolving in a circular orbit at a, height h from the earth surface, such that h << R, where R is the radius of the earth. Assuming that, the effect of earth’s atmosphere can be neglected, the minimum increase in the speed required so, that the satellite could escape from the, gravitational field of earth is:, (a), gR 2 1 (b) 2gR, , , , (c), , gR, , , , (d), , gR, 2, , from the surface of the moon? Assume that the, density of the earth and the moon are equal and, that the earth’s volume is 64 times the volume of, the moon:E, E, E, E, (a), (b), (c), (d), 16, 32, 64, 4, 113. Four identical particles of mass M are located, at the corners of a square of side ‘a’. What should, be their if each of them revolves under the, influence of other’s gravitational field in a circular, orbit circumscribing the square?, , GM, a, GM, (c) 1.16, a, (a) 1.21, , GM, a, GM, (d) 1.35, a, (b) 1.41, , 114. A solid sphere of mass ‘M’ and radius ‘a’ is, surrounded by a uniform concentric spherical shell, of thickness 2a and mass 2M. The gravitational, field at distance ‘3a’ from the centre will be:, GM, GM, 2GM, 2GM, (a), (b), (c), (d), 2, 2, 2, 3a, 9a, 9a, 3a 2, 115. The value of acceleration due to gravity at, Earth’s surface is 9.8 ms-2. The altitude above its, surface at which the acceleration due to gravity, decreases to 4.9 ms-2, is close to: (Radius of earth, = 6.4 x 106m), (a) 1.6 x 106 m (b) 6.4 x 106 m, (c) 9.0 x 106 m (d) 2.6 x 106 m, , 111. A satellite of mass M is in a circular orbit of, radius R about the centre of the earth. A meteorite, of the same mass, falling towards the earth,, collides with the satellite completely in elastically., The speeds of the satellite and the meteorite are, the same, just before the collision. The subsequent, motion of the combined body will be:, (a) In a circular orbit of a different radius, (b) In the same circular orbit of radius R, (c) In an elliptical orbit, (d) Such that it escapes to infinity, , 116. A spaceship orbits around a planet at a height, of 20 km from its surface. Assuming that only, gravitational field of the planet acts on the, spaceship, what will be the number of complete, revolutions made by the spaceship in 24 hours, around the planet?, [Given: Mass of planet = 8 x 1022 kg;, Radius of planet = 2 x 106 m,, Gravitational constant G = 6.67 x 10-11 Nm2/kg2], (a) 9, (b) 11, (c) 13, (d) 17, , 112. A rocket has to be launched from earth in such, a way that it never returns. If E is the minimum, energy delivered by the rocket launcher, what, should be the minimum energy that the launcher, should have if the same rocket is to be launched, , 117. The ratio of the weights of a body on the, Earth’s surface to that on the surface of a planet is, 1, 9 : 4. The mass of the planet is th of that of the, 9, Earth. If ‘R’ is the radius of the Earth, what is the, Page 10
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radius of the planet? (Take the planets to have the, same mass density), R, R, R, R, (a), (b), (c), (d), 9, 3, 2, 4, …..By Praveen Gupta, , Page 11
