Gravity and Gravitation — 50 MCQs

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

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

3. The gravitational force between two masses is always:

4. The SI unit of gravitational field strength is:

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

6. The SI unit of gravitational potential is:

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

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

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

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

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

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

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

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

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

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

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

18. 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?

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

20. 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:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

40. 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:

41. 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:

42. 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:

43. 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:

44. 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:

45. 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:

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

47. 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:

48. 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:

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

50. 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: