NEET UG - Escape velocity, motion of a satellite, orbital velocity, time period and energy of a satellite Question Bank with Options

1. The time period of a satellite in a circular orbit of radius r is given by \( T = 2\pi \sqrt{r^3/(GM)} \). If the radius of the orbit is increased by a factor of 4, the time period will increase by a factor of:

A) 2

B) 4

C) 8

D) 16

2. A satellite is in a circular orbit of radius r. If the gravitational force were suddenly removed, the satellite would:

A) Fall towards the Earth

B) Move in a straight line tangent to the orbit

C) Stop in its orbit

D) Move towards a higher orbit

3. The orbital velocity of a satellite is maximum when it is:

A) At apogee

B) At perigee

C) At the center of the orbit

D) In a circular orbit

4. A satellite is orbiting the Earth in a circular orbit. If its speed is reduced by 10%, it will:

A) Escape from orbit

B) Fall to Earth

C) Continue in the same orbit

D) Move to a higher elliptical orbit

5. The escape velocity from the surface of a planet of radius R and mass M is \( v_e \). If the planet's radius is halved and its mass is doubled, the new escape velocity will be:

A) \( v_e \)

B) \( 2 v_e \)

C) \( 4 v_e \)

D) \( v_e / 2 \)

6. Which of the following is conserved for a satellite in an elliptical orbit around the Earth?

A) Linear momentum

B) Angular momentum about the Earth's center

C) Kinetic energy

D) Potential energy

7. For a satellite in a circular orbit, the kinetic energy is K. The total energy is:

A) K

B) -K

C) 2K

D) -2K

8. The total energy of a satellite in an elliptical orbit of semi-major axis a is:

A) \( -GMa/(2a) \)

B) \( GMa/a \)

C) \( -GMa/a \)

D) \( GMa/(2a) \)

9. A satellite is in a circular orbit of radius R. If its energy is increased by \( \Delta E \), it moves to a higher orbit. The change in angular momentum is:

A) Zero

B) Positive

C) Negative

D) Depends on the new orbit

10. If the distance of a satellite from the center of the Earth is doubled, its orbital velocity will:

A) Double

B) Become half

C) Become \( 1/\sqrt{2} \) times

D) Become \( \sqrt{2} \) times

11. The time period of a satellite in a circular orbit of radius r is proportional to:

A) r

B) r^2

C) r^{3/2}

D) r^{1/2}

12. For a satellite in a circular orbit, the velocity is given by \( v_o = \sqrt{GM/(R+h)} \). The acceleration due to gravity at that height is \( g' = GM/(R+h)^2 \). The orbital velocity can also be written as:

A) \( \sqrt{g'(R+h)} \)

B) \( \sqrt{g'R} \)

C) \( \sqrt{g'/(R+h)} \)

D) \( \sqrt{g'/(R+2h)} \)

13. A satellite is launched into a circular orbit of radius R around the Earth. To transfer it to a circular orbit of radius 2R, the energy required is:

A) Positive

B) Negative

C) Zero

D) Infinite

14. The minimum velocity with which a body must be projected vertically upwards from the surface of the Earth to escape Earth's gravitational field is called:

A) Orbital velocity

B) Escape velocity

C) Terminal velocity

D) Critical velocity

15. If a satellite is in an orbit of radius r, its kinetic energy is proportional to:

A) r

B) 1/r

C) \( r^2 \)

D) 1/\( r^2 \)

16. The orbital velocity of a satellite in a circular orbit of radius R is \( v_o \). If the radius is increased to 2R, the new orbital velocity is:

A) \( v_o / \sqrt{2} \)

B) \( v_o / 2 \)

C) \( v_o \)

D) \( \sqrt{2} v_o \)

17. For a geostationary satellite, the angular velocity is:

A) Equal to the angular velocity of Earth's rotation

B) Twice the angular velocity of Earth's rotation

C) Half the angular velocity of Earth's rotation

D) Zero

18. The total energy of a satellite in a circular orbit of radius r is E. If the radius is increased to 2r, the new total energy will be:

A) E/2

B) 2E

C) E/4

D) 4E

19. A satellite is in a circular orbit. If the radius of the orbit increases, the orbital velocity:

A) Increases

B) Decreases

C) Remains constant

D) Becomes zero

20. The escape velocity from a planet of mass M and radius R is given by:

A) \( \sqrt{GM/R} \)

B) \( \sqrt{2GM/R} \)

C) \( \sqrt{GM/(2R)} \)

D) \( GM/R \)

21. The orbital radius of a satellite is R. If the radius of the orbit is increased to 4R, the time period of revolution will change by a factor of:

A) 1/8

B) 1/4

C) 8

D) 4

22. A satellite is in an elliptical orbit. Its speed at perigee is greater than its speed at apogee because:

A) The distance from Earth is smaller at perigee

B) The distance from Earth is larger at perigee

C) The gravitational force is weaker at perigee

D) The angular momentum is larger at perigee

23. If the Earth suddenly shrinks to half its radius without changing its mass, the escape velocity from the surface will:

A) Remain the same

B) Become double

C) Become half

D) Become four times

24. The kinetic energy of a satellite in a circular orbit of radius r is \( K \). Its potential energy is:

A) \( -K \)

B) \( 2K \)

C) \( -2K \)

D) \( K/2 \)

25. For a satellite to orbit the Earth, its orbital velocity must be:

A) Less than escape velocity

B) Equal to escape velocity

C) Greater than escape velocity

D) Zero

26. The time period of a satellite orbiting close to the Earth's surface is approximately:

A) 85 minutes

B) 24 hours

C) 12 hours

D) 1 hour

27. A satellite is in a circular orbit of radius R. If it jumps to a circular orbit of radius 2R, the ratio of its new orbital velocity to the original orbital velocity is:

A) 1/2

B) 1/\( \sqrt{2} \)

C) \( \sqrt{2} \)

D) 2

28. The orbital speed of a satellite in a circular orbit of radius r around the Earth is \( v_o \). The escape speed from the same orbit is \( v_e \). The relation between them is:

A) \( v_e = v_o \)

B) \( v_e = \sqrt{2} v_o \)

C) \( v_o = \sqrt{2} v_e \)

D) \( v_e = 2 v_o \)

29. Which of the following statements is true for a satellite in an elliptical orbit?

A) Angular momentum is not conserved

B) Total energy is zero

C) Speed is constant

D) Angular momentum is conserved

30. The energy required to move a satellite from an orbit of radius \( r_1 \) to an orbit of radius \( r_2 \) (\( r_2 > r_1 \)) is:

A) \( GMm(1/r_2 - 1/r_1) \)

B) \( GMm(1/r_1 - 1/r_2) \)

C) \( -GMm(1/r_2 - 1/r_1) \)

D) \( -GMm(1/r_1 - 1/r_2) \)

31. A satellite is in a circular orbit around the Earth. If its speed is increased, it will move to:

A) A circular orbit of smaller radius

B) A circular orbit of larger radius

C) An elliptical orbit

D) Escape from Earth's gravity

32. If the radius of Earth were to decrease by 1%, its mass remaining the same, then the escape velocity would:

A) Increase by 1%

B) Decrease by 1%

C) Increase by 0.5%

D) Decrease by 0.5%

33. For a satellite in a circular orbit, the time period T is related to the orbital radius r by:

A) T \( \propto r^{1/2} \)

B) T \( \propto r^{3/2} \)

C) T \( \propto r^{-1/2} \)

D) T \( \propto r^{-3/2} \)

34. The orbital velocity of a satellite is given by \( v_o = \sqrt{GM/(R+h)} \). If h approaches zero, the orbital velocity becomes:

A) \( \sqrt{GM/R} \)

B) \( \sqrt{gR} \)

C) \( \sqrt{2gR} \)

D) \( \sqrt{GM} \)

35. Escape velocity depends on the mass of:

A) The object being projected

B) The celestial body from which it is projected

C) Both the object and the celestial body

D) Neither the object nor the celestial body

36. The potential energy of a satellite in a circular orbit of radius r is proportional to:

A) 1/r

B) r

C) -1/r

D) -r

37. The kinetic energy of a satellite in a circular orbit of radius r is proportional to:

A) 1/r

B) r

C) 1/\( \sqrt{r} \)

D) \( \sqrt{r} \)

38. If a satellite is in an elliptical orbit, its speed is:

A) Maximum at apogee

B) Minimum at perigee

C) Maximum at perigee

D) Constant throughout the orbit

39. What is the condition for a satellite to be in a geostationary orbit?

A) It must orbit from west to east

B) Its time period must be 24 hours

C) Its orbital plane must be equatorial

D) All of the above

40. The ratio of escape velocity to orbital velocity for a satellite at the surface of the Earth is:

A) 1/\( \sqrt{2} \)

B) \( \sqrt{2} \)

C) 2

D) 1/2

41. If a satellite is moved from a lower orbit to a higher orbit, its:

A) Potential energy decreases

B) Kinetic energy increases

C) Total energy decreases

D) Total energy increases

42. The total energy of a satellite revolving in a circular orbit of radius r around the Earth is:

A) \( -GMm/(2r) \)

B) \( GMm/r \)

C) \( -GMm/r \)

D) \( GMm/(2r) \)

43. The orbital velocity of a satellite is independent of:

A) Mass of the planet

B) Radius of the orbit

C) Mass of the satellite

D) Gravitational constant

44. A geostationary satellite orbits the Earth at a height of approximately:

A) 100 km

B) 1000 km

C) 36000 km

D) 100000 km

45. For a geostationary satellite, the time period of revolution is:

A) 6 hours

B) 12 hours

C) 24 hours

D) 36 hours

46. The orbital velocity of a satellite at a height h above the Earth's surface is given by:

A) \( \sqrt{GM/R} \)

B) \( \sqrt{GM/(R+h)} \)

C) \( \sqrt{GM/(R+2h)} \)

D) \( \sqrt{gR} \)

47. A satellite is revolving around a planet in a circular orbit. If the velocity of the satellite is suddenly increased by 50%, it will:

A) Escape from the orbit

B) Fall back to the planet

C) Continue to orbit in the same orbit

D) Move to a higher elliptical orbit

48. If the escape velocity from the surface of the Earth is 11.2 km/s, the escape velocity from a planet of mass and radius double that of Earth is:

A) 5.6 km/s

B) 11.2 km/s

C) 22.4 km/s

D) 44.8 km/s

49. The escape velocity from a planet of radius R and density \( \rho \) is proportional to:

A) R \( \sqrt{\rho} \)

B) R \( \rho \)

C) R / \( \sqrt{\rho} \)

D) R / \( \rho \)

50. What is the escape velocity of an object on the surface of the Earth?

A) 6.4 km/s

B) 11.2 km/s

C) 16.0 km/s

D) 22.4 km/s

Escape velocity, motion of a satellite, orbital velocity, time period and energy of a satellite - Question Bank