Gravity and Gravitation — 75 MCQs

1. According to Newton's law of gravitation, the gravitational force between two point masses is inversely proportional to:

2. The Moon's mass is about 1/81 that of the Earth, and the Earth-Moon distance is d. At what distance from the Earth (measured along the line joining them) does the net gravitational field due to the Earth and Moon become zero?

3. The SI value of the universal gravitational constant G is approximately:

4. A satellite's orbital radius is reduced to half its original value. Its orbital velocity:

5. The gravitational force between two masses is always:

6. Along the axis of a uniform ring of mass M and radius R, the gravitational field strength E(x) at a distance x from the centre (along the axis) is E(x) = GMx/(R² + x²)^(3/2). At what value of x is this field strength maximum?

7. The SI unit of gravitational field strength is:

8. If both masses in a gravitating pair are doubled and the distance between them is halved, the new gravitational force is how many times the original?

9. The relation connecting acceleration due to gravity g, the universal gravitational constant G, the mass of the Earth M, and its radius R is:

10. Two planets have the same average density but different radii R₁ and R₂. The ratio of their surface gravitational accelerations g₁:g₂ is:

11. The SI unit of gravitational potential is:

12. A narrow frictionless tunnel is drilled straight through the centre of the Earth (assumed a uniform sphere of density ρ, radius R, surface gravity g). A ball is dropped into the tunnel from the surface. Its subsequent motion is:

13. The gravitational potential energy of a bound two-mass system is always:

14. If the Earth's radius were halved while its mass remained unchanged, the new surface value of g would become:

15. As altitude above the Earth's surface increases, the value of g:

16. The value of the universal gravitational constant G was first experimentally determined by:

17. As depth below the Earth's surface increases, the value of g:

18. Due to the Earth's rotation about its own axis, the apparent weight of a body at the equator is less than its true weight. If ω is the Earth's angular velocity and R its radius, the reduction in the effective value of g at the equator is:

19. If the distance between two point masses is doubled, the gravitational force between them becomes:

20. At the exact centre of the Earth, the value of g is:

21. A hypothetical planet has twice the mass and twice the radius of Earth. Compared to Earth's escape velocity vₑ, the escape velocity from this planet's surface is:

22. The centre of mass of a system of particles depends only on:

23. A satellite is projected horizontally from a point at distance r from a planet's centre with a speed v that is less than the circular orbital velocity v₀ at that radius. The resulting orbit is an ellipse in which the point of projection is:

24. The centre of gravity of a body depends on:

25. Two satellites orbit the same planet at radii r and 4r respectively. The ratio of their time periods T(4r):T(r) is:

26. The orbital velocity of a satellite in a circular orbit of radius r around a planet of mass M is given by:

27. The gravitational field strength at a distance of 2R from the centre of a planet of radius R (surface gravity g) is:

28. A satellite is projected horizontally from a point at distance r with a speed v such that v₀ < v < vₑ (greater than the local circular velocity but less than the local escape velocity). The point of projection is then the orbit's:

29. The escape velocity from a planet's surface, expressed in terms of g and R, is:

30. Two identical point masses m are fixed at the two ends of a light rod of length d. A third mass is placed exactly at the midpoint of the rod. The net gravitational force on the third mass due to the two end masses is:

31. For a satellite to be geostationary, its time period must equal:

32. The value of g at a height equal to the Earth's radius R above the surface (i.e. at a distance 2R from the centre) is:

33. The time period of a satellite orbiting very close to the surface of a planet (r ≈ R) depends only on:

34. The value of g at a depth of R/2 below the Earth's surface (uniform-density approximation) is:

35. A planet has the same mean density as the Earth but a radius twice that of the Earth. The ratio of the escape velocity from this planet's surface to that from the Earth's surface is:

36. The ratio of escape velocity to orbital velocity at the same radius is:

37. If the orbital radius of a satellite is increased to 4 times its original value, its orbital velocity becomes:

38. A planet moves in an elliptical orbit around the Sun. Its distances from the Sun at perihelion and aphelion are in the ratio rₚ : rₐ = 1 : 2. The ratio of its orbital speeds vₚ : vₐ at these two points is:

39. If the orbital radius of a satellite is increased to 4 times its original value, its time period becomes:

40. Using the exact (non-approximated) expression for variation of g with altitude, the height above the Earth's surface at which g reduces to exactly one-fourth of its surface value is:

41. If the orbital radius of a satellite is doubled, its kinetic energy becomes:

42. A satellite in a low circular orbit experiences a small amount of atmospheric drag, which does negative work on it over many orbits. As the satellite's orbit gradually shrinks as a result, its orbital speed:

43. If the orbital radius of a satellite is doubled, the magnitude of its potential energy becomes:

44. A satellite of mass 500 kg orbits the Earth in a circular orbit of radius 7.0 × 10⁶ m. Calculate the energy required to raise it to a new circular orbit of radius 1.4 × 10⁷ m. (M_Earth = 6.0 × 10²⁴ kg, G = 6.674 × 10⁻¹¹ N m² kg⁻²)

45. The total mechanical energy E of an orbiting satellite is related to its kinetic energy KE by:

46. The binding energy of a satellite of mass m orbiting at radius r around a planet of mass M is given by:

47. The approximate height of a geostationary orbit above the Earth's surface is:

48. The approximate orbital period of a typical GPS satellite is:

49. The minimum number of GPS satellites a receiver must detect simultaneously to determine its full three-dimensional position and correct its own clock is:

50. A rocket is launched vertically from the Earth's surface with a speed greater than the escape velocity vₑ. Neglecting the Earth's rotation and atmospheric resistance, its speed when it is very far from the Earth (in terms of its launch speed v and vₑ) is:

51. The centre of mass and centre of gravity of a body coincide when:

52. In the vector form of Newton's law of gravitation, the negative sign indicates that the force is:

53. The approximate escape velocity from the Earth's surface is:

54. The gravitational potential at an infinite distance from any mass is taken to be:

55. Two stars of masses m and 2m, separated by a fixed distance d, orbit their common centre of mass. Their common orbital time period is:

56. For the same binary star system (masses m and 2m, separated by distance d, orbiting their common centre of mass), the ratio of the orbital radius of the lighter star (r₁) to that of the heavier star (r₂) is:

57. A satellite orbits a planet of mass M at radius r with time period T. An identical satellite orbits a different planet of mass 4M at the same orbital radius r. Its time period will be:

58. The orbital radius of a satellite is increased by exactly 1%, with no other quantities changed. Using the relation T² ∝ r³, the approximate percentage increase in its time period is:

59. An astronaut inside a satellite orbiting the Earth experiences apparent weightlessness. The correct physical explanation for this is:

60. A straight frictionless tunnel is drilled through a uniform-density Earth along a chord that does NOT pass through the centre. A ball released from one end of this tunnel will:

61. Three point masses, each of mass m, are placed at the corners of an equilateral triangle of side a. The total gravitational potential energy of this three-mass system is:

62. A satellite orbits a planet in a circular orbit of radius 1.0 × 10⁷ m with a time period of 1.0 × 10⁴ s. Using Kepler's third law, estimate the mass of the planet. (G = 6.674 × 10⁻¹¹ N m² kg⁻²)

63. A body is projected from the Earth's surface with exactly the escape velocity vₑ, directed vertically upward. Ignoring air resistance and the Earth's rotation, its trajectory as it recedes to infinity is best described as:

64. A planet moves in a circular orbit around a star. If the gravitational force of attraction were instead to vary as 1/r³ rather than 1/r² (with all other conditions unchanged), which relation between orbital speed v and radius r would then hold for a stable circular orbit?

65. A body weighs W newtons at the Earth's surface. If it is taken to a height equal to the Earth's radius R above the surface, its weight becomes:

66. A satellite is revolving around the Earth in an orbit of radius r with time period T. If the same satellite is to be placed in an orbit of radius 4r, its new time period T′ is related to the original as:

67. Two identical satellites, each of mass m, orbit the Earth in the same circular orbit of radius r but in exactly opposite directions. They collide head-on and stick together (a perfectly inelastic collision). Immediately after the collision, the combined wreckage (mass 2m) will:

68. The gravitational field strength E(r) inside a uniform solid sphere of mass M and radius R (for r < R) and outside it (for r > R) are correctly described, respectively, by:

69. The energy that must be supplied to raise a satellite of mass m from a circular orbit of radius r to a circular orbit of radius 2r, around a planet of mass M, is:

70. Using the formula for variation of g with depth, the depth below the Earth's surface at which g reduces to exactly half its surface value is:

71. Regarding the relativistic time corrections applied to GPS satellite clocks, which statement is correct?

72. If the mass of a planet is doubled while a satellite's orbital radius r is kept unchanged, the satellite's new orbital velocity becomes:

73. A satellite is placed in a circular equatorial orbit at a radius smaller than the geostationary radius, moving in the same direction as the Earth's rotation. Relative to a fixed point on the Earth's surface, this satellite will appear to:

74. As the orbital radius r of a satellite decreases, its binding energy:

75. A hypothetical planet has twice the mass of Earth and half the radius of Earth. The escape velocity from this planet's surface, compared to Earth's escape velocity vₑ, is: