NEET AIPMT Physics Chapter Wise Solutions – Gravitation
1. 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-1, then the orbital speed of the satellite is
(a) 9.13 km s-1
(b) 6.67 km s-1
(c) 7.76 km s-1
(d) 8.56 km s-1(AIPMT 2015)
2. 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,
(a) the linear momentum of S remains constant in magnitude.
(b) the acceleration of S is always directed towards the centre of the earth.
(c) the angular momentum of S’ about the centre of the earth changes in direction, but its magnitude remains constant.
(d) the total mechanical energy of S varies periodically with time. (AIPMT 2015)
3. Kepler’s third law states that square of period of revolution (7) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T2 = Kr3 here K is constant.
If the masses of sun and planet are M and m respectively then as per Newton’s law of gravitation force of attraction between them is F= here G is gravitational constant. r
The relation between G and K is described as
4. Two spherical bodies of mass M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is
(a) 7.5 R
(b) 1.5 R
(c) 2.5 R
(d) 4.5 R (AIPMT 2015,Cancelled)
5. 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 (mass = 5.98 x 1024 kg) have to be compressed to be a black hole?
(b) 10-6 m
(c) 10-2 m
(d) 100 m (AIPMT 2014)
6. Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by
7. Infinite number of bodies, each of mass 2 kg are situated onx-axis at distances 1 m, 2 m, 4 m, 8 m,…, respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
8. 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
9. The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, then
10. A particle of mass ‘m ’ is kept at rest at a height 3R from the surface of earth, where ‘R’ is radius of earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is
(g is acceleration due to gravity on the surface of earth)
11. The height at which the weight of a body becomes its weight on the surface of earth (radius R), is
(c) 3 R
(d) AR (Prelims 2012)
12. A spherical planet has a mass MP and diameter DP. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to
13. A geostationary satellite is orbiting the earth at a height of 5R above that surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is
14. If ve is escape velocity and v0 is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by
15. Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)
16. A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If v1 and v2 are the linear velocities at these points respectively, then the ratio is
(d) r1/r2 (Prelims 2011)
17. A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the . earth. The minimum value of u so that the particle does not return back to earth, is
18. A particle of mass 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
19. The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3V, then the speed of satellite B will be
20. A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be
(a) 9.9 m
(c) 10 m
(d) 20 m (Prelims 2010)
21. The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1, to another of radius R2(R2> R1) is
22. The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below
23. (1) Centre of gravity (C.G) of a body is the point at which the weight of the body acts
(2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius.
(3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G
(4) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G of the body to the axis. Which one of the following pairs of statements is correct?
(a) (4) and (1)
(c) (2) and (3)
(d) (3) and (4) (Mains 2010)
24. The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t1 is the time for the planet to move from C to D and t2 is the time to move from A to B then
25. Two satellites of earth, ,S1 and S2are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?
(a) The potential energies of earth and satellite in the two cases are equal.
(b) S1 and S2 are moving with the same speed.
(c) The kinetic energies of the two satellites are equal.
(d) The time period of S1 is four times that of S2. (2007)
26. The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fV, where v is its escape velocity from the surface of the Earth. The value of f is
27. 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
28. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is
(d) 75 (2005)
29. The density of a newly discovered planet is twice that of 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 R, the radius of the planet would be
30. Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be
(a) 3 F
(d) F19 (2003)
31. The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B ?
(d) (2/3) m (2003)
32. A body of mass m is placed on earth surface which is taken from earth surface to a height of h = 3R, then change in gravitational potential energy is
33. With what velocity should a particle be projected so that its height becomes equal to radius of earth?
34. For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth. Then escape velocity for this planet will be
(a) 11.2 km/sec
(b) 22.4 km/sec
(c) 5.6 km/sec
(d) 44.8 km/sec. (2000)
35. Gravitational force is required for
(a) stirring of liquid
(d) radiation. (2000)
36. A body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then gravitational force exerted on it will be
(a) 36 N
(b) 32 N
(c) 144 N
(d) 50 N. (2000)
37. The escape velocity of a sphere of mass m is given by (G = Universal gravitational constant; Me = Mass of the earth and Re– Radius of the earth
38. The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth’s mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes
(a) 22.4 km/s
(b) 44.8 km/s
(c) 5.6 km/s
(d) 11.2 km/s. (1997)
39. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?
(d) 3. (1997)
40. What will be the formula of mass of the earth in terms of g, R and G ?
41. A ball is dropped from a spacecraft revolving around the earth at a height of 120 km. What will happen to the ball?
(a) it will fall down to the earth gradually
(b) it will go very far in the space
(c) it will continue to move with the same speed along the original orbit of spacecraft
(d) it will move with the same speed, tangentially to the spacecraft. (1996)
42. The acceleration due to gravity g and mean density of the earth p are related by which of the following relations? (where G is the gravitational constant and R is the radius of the earth.)
43. Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is
44. The earth (mass = 6 × 1024 kg) revolves around the sun with an angular velocity of 2 x 10-7 rad’s in a circular orbit of radius 1.5 x 108 km. The force exerted by the sun on the earth, in newton, is
45. The radius of earth is about 6400 km and that of mars is 3200 km. The mass of the earth is about 10 times mass of mars. An object weighs 200 N on the surface of earth. Its weight on the surface of mars will be
(a) 20 N
(b) 8 N
(c) 80 N
(d) 40 N. (1994)
46. The distance of two planets from the sun are 1013m and 1012m respectively. The ratio of time periods of the planets is
47. If the gravitational force between two objects were proportional to MR (and not as MR2), where R is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed v, proportional to
(b) R° (independent of R)
(d) MR. (1994, 89)
48. A satellite in force free space sweeps stationary interplanetary dust at a rate of dM/dt = av, where M is mass and v is the speed of satellite and a is a constant. The acceleration pf satellite is
49. The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is
50. A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth’s centre. Their time periods are in the ratio of
(a) 1 : 2
(b) 1 : 16
(c) 1 :32
(d) 1:2V2 (1993)
51. The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth’s surface is g. What will be the radius of the orbit of a geostationary satellite ?
52. The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy ?
53. A planet is moving in an elliptical orbit around the sun. If T, V, E and L stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct ?
(a) T is conserved
(b) V is always positive
(c) E is always negative
(d) L is conserved but direction of vector L changes continously. (1990)
54. For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60° with the vertical, then escape velocity will be
55. The largest and the shortest distance of the earth from the sun are rl and r2. Its distance from the sun when it is at perpendicular to the major- axis of the orbit drawn from the sun is