Title 8. Gravitation.pdf ✅

1. A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at 2 a distance from the centre, will be :- 2. In order to shift a body of mass m from a circular orbit of radius 3R to a higher radius 5R around the earth, the work done is :- 3. The maximum vertical distance through which a fully dressed astronaut can jump on the earth is 0.5 m. If mean density of the moon is two-thirds that of the earth and radius is one quarter that of the earth, the maximum vertical distance through which he can jump on the moon and the ratio of time of duration of jump on the moon to that on the earth are : (1) 3 m, 6 : 1 (2) 6 m, 3 : 1 (3) 3 m, 1 : 6 (4) 6 m, 1 : 6 4. Two equal masses m and m are hung from a balance whose scale pans differ in vertical height by 'h'. The error in weighing in terms of density of the earth  is :- 5. In both figures shown below a hole along the diameter of earth. In first, a particle is released from A and it oscillated with time period T1. In second figure, same particle is released from point B and it oscillates with time period T2 then [O is centre of earth] :- 6 . The self gravitational potential energy of a spherical shell of mass M and radius R is– 7 . Mass density of a solid sphere is . Radius of the sphere is R. The gravitational field at a distance r from the centre of the sphere inside it is– 8 . A satellite is revolving round the earth with orbital speed 0. If it stops suddenly, the speed with which it will strike the surface of earth would be : (e = escape velocity of a particle on earth's surface) 9. Two satellites A and B, having ratio of masses 3 : 1 are in circular orbits of radius r and 4r. Calculate the ratio of total mechanical energy of A and B. (1) 3 : 4 (2) 12 : 1 (3) 4 : 3 (4) 1 : 12 10. The value of escape velocity on a certain planet is 2 km/s. Then the value of orbital speed for a satellite orbiting close to its surface is : (1) 12 km/s (2) 1 km/s (3) 2 km/s (4) 2 2 km/s 11. A satellite of mass m is in a circular orbit of radius2R about the earth. How much energy is required to transfer it to a circular orbit of radius 4R :-(R = Radius of earth) Gravitation
12. If the radius of earth reduces by 4% and density remains same then escape velocity will- (1) reduce by 2% (2) increase by 2% (3) reduce by 4% (4) increase by 4% A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion. B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion. C. If Assertion is True but the Reason is False. D. If both Assertion & Reason are False. 13. Assertion :- There is no effect of rotation of earth on acceleration due to gravity at poles. Reason :- Rotation of earth is about polar axis. (1) A (2) B (3) C (4) D 14. The time period of a satellite of earth is 5 hours. If the separation between the centre of earth and the satellite is increased to 4 times the previous value, the new time period will become :- (1) 10 h (2) 80 h (3) 40 h (4) 20 h 15. Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is :- 16. 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 hare much smaller than the radius of earth, then which one of the following is correct ? (1) 2 h d = (2) 3 2 h d = (3) d h = 2 (4) d = h 17. A certain object is projected vertically from the surface of the earth of radius R with a velocity equal to half the escape velocity. The maximum height attained by the object will be (1) R/3 (2) 2R (3) 3R (4) 6R 18. A body is dropped from a satellite in parking orbit. Which of the following describes its behavior correctly? (1) It will be stationary in the space. (2) It will fall towards the earth. (3) It will rotate about the axis of the earth with a time period of 24 hours. (4) It will rotate about the earth with a time period of 8 hours. 19. Suppose the earth stopped rotating. Then, the weight a body will (1) Increase equally at all points (2) Decrease equally at all points (3) Increase at the equator (4) Increase at the poles 20. A particle falls from infinity to the earth. Its velocity on reaching the earth of radius R is 21. The period of a satellite, in a circular orbit near an equatorial plane, will not depend on (1) The mass of the planet (2) The radius of the planet (3) The mass of the satellite (4) All the above parameters 22. Weightlessness experienced while orbiting the earth in space-ship, is the result of (1) Inertia (2) Acceleration (3) Zero gravity (4) Free fall towards earth 23. Two identical solid copper spheres of radius R placed in contact with each other. The gravitational attraction between them is proportional to (1) R2 (2) R–2 (3) R4 (4) R–4
24. Two planets have the same average density but their radii are R1 and R2. If acceleration due to gravitation these planets be g1 and g2 respectively, then 25. Energy required to move a body of mass m from an orbit of radius 4R to 6R is 26. Four particles of equal mass M move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is: 27. Suppose the gravitational force varies inversely as the nth power of the distance. Then, the time period of a planet in circular orbit of radius R around the sun will be proportional to : (1) Rn (2) R(n+1)/2 (3) R(n–1)/2 (4) R–n 28. The speed of the earth's rotation about its axis is . Its speed is increased to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is : (1) 1 (2) 8.5 (3) 17 (4) 34 29. If mass M is split into two parts m and (M – m)which are then separated by a distance, the ratio of mass m/M that maximizes the gravitational force between the two parts is: (1) 1 : 2 (2) 1 : 1 (3) 2 : 1 (4) 1 : 4 30. A planet revolves in elliptical orbit around the sun. The linear speed of the planet will be maximum at (1) A (2) B (3) C (4) D 31. A satellite is orbiting around the earth with a period T. If the earth suddenly shrinks to half its radius without change in mass, the period of revolution of the satellite will be: (1) 2 T (2) 2 T (3) T (4) 2T 32. According to Kepler's law, the period of revolution of a planet (T) and its mean distance from the sun (R) are related by the equation: (1) T2R = constant (2) T2R -3 = constant (3) TR3 = constant (4) T2R3 = constant 33. The given figure shows the motion of a planet around the sun S in an elliptical orbit with the sun at the focus. The shaded areas A and B are also shown in the figure which can be assumed to be equal. If t1 and t2 represent the time taken for the planet to move from a to b and c to d respectively, then (1) t1< t2 (2) t1> t2 (3) t1 = t2 (4) from the given information the relation 34. Orbital velocity of an object of mass m is proportional to : (1) m0 (2) m (3) m2 (4) 1 m 35. Two particles of combined mass M, placed in space with certain separation, are released. Interaction between the particles is only of gravitational in nature and there is no external force present. Acceleration of one particle with respect to the other when separation between them is R, has a magnitude :
(4) not possible to calculate due to lack of Information 36. A simple pendulum is taken to 64 km above the earth's surface. It's time period will: (1) increase by 1 % (2) decrease by 1 % (3) increase by 2 % (4) decrease by 2 % 37. A satellite is seen after each 8 hours over equator at a place on the earth when its sense of rotation is opposite to the earth. The time interval after which it can be seen at the same place when the sense of rotation of earth &satellite is same will be: (1) 8 hours (2) 12 hours (3) 24 hours (4) 6 hours 38. If the apparent weight of the bodies at the equator is to be zero, then the earth should rotate with angular velocity 39. If g be the acceleration due to gravity of the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is : (1) (1/2) mgR (2) 2 mgR (3) mgR (4) (1/4) mgR 40. A ball of mass m is thrown from surface of a planet of mass M, radius R at angle 60° with vertical. The minimum speed required so that ball escape from that planet is– 41. Five bodies of mass m,m,m,m,m0 placed at corners of a pentagon as shown in figure. The net gravitational force on body of mass 'm' placed at centre is– 42. Two bodies of masses M and 9M are placed at distance r. The gravitation field intensity at the position of mass M is E then gravitational field intensity at the position of 9M is– (1) E (2) 9E (3) 9 E (4) 1 43. Two satellites of mass 50 kg and 100 kg revolve around the earth in circular orbit of radius 9Rand 16 R respectively, where R is the radius of earth. The speeds of the two satellites will be in the ratio :- 44. The mass of planet is 1 9 of the mass of the earth and its radius is half that of the earth. If a bodyweight 9N on the earth. Its weight on the planet would be :- (1) 4 N (2) 4.5 N (3) 6 N (4) None of these 45. The weight of a man in a lift moving upwards is608 N. While the weight of the same man in the lift moving downwards with the same acceleration is 368 N. His normal weight is :- (1) 480 N (2) 588 N (3) 488 N (4) 240 N 46. Escape velocity at the surface of earth is 11.2 km/sec. If radius of planet is double that of earth but mean density same as that of earth then the escape velocity will be :- (1) 11.2 km/sec (2) 5.5 km/sec (3) 15.5 km/sec (4) 22.4 km/sec