JEE Main - Escape velocity and motion of satellites Online Test (MCQ Quiz)

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

A) 6.2 km/s B) 11.2 km/s C) 16.2 km/s D) 21.2 km/s

2. The escape velocity from a planet depends on:

A) The mass of the planet only B) The radius of the planet only C) The mass and radius of the planet D) The mass and density of the planet

3. If the radius of a planet is halved, what happens to the escape velocity from its surface, assuming its density remains the same?

A) It remains the same B) It doubles C) It becomes half D) It becomes one-fourth

4. Which of the following factors does NOT affect the escape velocity from the surface of a celestial body?

A) Gravitational constant (G) B) Mass of the celestial body (M) C) Radius of the celestial body (R) D) None of the above

5. The escape velocity from the surface of the Earth is approximately:

A) 7.9 km/s B) 11.2 km/s C) 16.6 km/s D) 22.4 km/s

6. For a satellite orbiting the Earth at a height h above the surface, its orbital velocity is given by:

A) v_o = sqrt(GM/R) B) v_o = sqrt(GM/(R+h)) C) v_o = sqrt(GM(R+h)) D) v_o = sqrt(GM/h)

7. What is the relationship between escape velocity (v_e) and orbital velocity (v_o) for a satellite orbiting at the surface of a planet?

A) v_e = v_o B) v_e = sqrt(2) * v_o C) v_e = 2 * v_o D) v_e = v_o / sqrt(2)

8. If a satellite is launched with a velocity greater than escape velocity, it will:

A) Orbit the Earth in an elliptical path B) Orbit the Earth in a circular path C) Escape from Earth's gravitational pull D) Fall back to Earth

9. The time period of a satellite orbiting the Earth in a circular orbit of radius r is proportional to:

A) r B) r^2 C) r^(3/2) D) r^(-3/2)

10. For a geostationary satellite, its time period of revolution is:

A) 6 hours B) 12 hours C) 24 hours D) 48 hours

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

A) 100 km B) 1000 km C) 36000 km D) 100000 km

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

A) Apogee B) Perigee C) The highest point of its orbit D) The lowest point of its orbit

13. The kinetic energy of a satellite in a circular orbit is given by:

A) GMm/(2R) B) GMm/R C) GMm/(4R) D) GMm/(R+h)

14. The total energy of a satellite in a circular orbit of radius r is:

A) GMm/r B) -GMm/r C) GMm/(2r) D) -GMm/(2r)

15. If a satellite is moved from a lower orbit to a higher orbit, its total energy:

A) Decreases B) Increases C) Remains the same D) Becomes zero

16. Which of the following is a condition for a satellite to be in a geostationary orbit?

A) It must orbit in the equatorial plane. B) Its time period must be 12 hours. C) It must orbit from East to West. D) Its altitude must be 10000 km.

17. The escape velocity from the Moon is approximately:

A) 1.12 km/s B) 2.38 km/s C) 5.1 km/s D) 11.2 km/s

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

A) Constant throughout the orbit B) Maximum at apogee C) Minimum at perigee D) Maximum at perigee

19. What is the unit of escape velocity?

A) m/s^2 B) m/s C) Joule D) kg/m^3

20. The formula for escape velocity from the surface of a celestial body of mass M and radius R is:

A) sqrt(GM/R) B) sqrt(2GM/R) C) sqrt(GM/(2R)) D) sqrt(2GM/(2R))

21. If the mass of a planet is M and its radius is R, the escape velocity from its surface is proportional to:

A) M^(1/2) R^(-1/2) B) M^(1/2) R^(1/2) C) M^(-1/2) R^(1/2) D) M R^(-1)

22. Consider a satellite in a circular orbit. If its speed is increased slightly, it will:

A) Move to a higher circular orbit B) Move to a lower circular orbit C) Escape from the orbit D) Move to an elliptical orbit

23. The orbital period of a satellite depends on:

A) Its mass B) The mass of the planet C) The radius of the orbit D) Both the mass of the planet and the radius of the orbit

24. A satellite is in a circular orbit around Earth. If its orbital radius is increased, its time period will:

A) Decrease B) Increase C) Remain the same D) Become zero

25. The condition for a satellite to be in a stable circular orbit is that the gravitational force provides the necessary:

A) Centrifugal force B) Centripetal force C) Tension force D) Frictional force

26. What is the angular velocity of a geostationary satellite?

A) pi/12 rad/hr B) pi/24 rad/hr C) 2pi/24 rad/hr D) 2pi/12 rad/hr

27. If the Earth's radius were halved, keeping its mass the same, the escape velocity from its surface would:

A) Remain the same B) Double C) Become half D) Become four times

28. The kinetic energy of a satellite in an elliptical orbit is:

A) Constant B) Maximum at perigee C) Minimum at apogee D) Maximum at apogee

29. The potential energy of a satellite in a circular orbit of radius r is:

A) GMm/r B) -GMm/r C) GMm/(2r) D) -GMm/(2r)

30. If a satellite is launched with a velocity less than the escape velocity but greater than the orbital velocity, it will follow:

A) A circular orbit B) An elliptical orbit C) A parabolic path D) A hyperbolic path

31. The direction of the velocity of a satellite in a circular orbit is always:

A) Towards the center of the Earth B) Away from the center of the Earth C) Tangent to the orbit D) Perpendicular to the tangent of the orbit

32. A satellite is in a circular orbit of radius R around the Earth. If its speed is suddenly doubled, what will happen?

A) It will escape Earth's gravity. B) It will move to a higher circular orbit. C) It will fall back to Earth. D) It will enter an elliptical orbit and escape.

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

A) The mass of the planet B) The radius of the orbit C) The mass of the satellite D) The gravitational constant

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

A) Equal to escape velocity B) Less than escape velocity but greater than zero C) Equal to orbital velocity D) Greater than escape velocity

35. What is the minimum velocity required to put a satellite into a circular orbit just above the Earth's surface?

A) 7.9 km/s B) 11.2 km/s C) 16.6 km/s D) 22.4 km/s

36. If a satellite is in an elliptical orbit, its angular momentum is conserved because:

A) The gravitational force is conservative. B) The gravitational force is central. C) The orbit is stable. D) The velocity is constant.

37. The orbital radius of a geostationary satellite is approximately:

A) 42,000 km B) 36,000 km C) 64,000 km D) 10,000 km

38. If the mass of the Earth is M and its radius is R, the escape velocity is proportional to:

A) M/R B) M/R^2 C) M/sqrt(R) D) sqrt(M)/R

39. Which of the following statements is TRUE for a satellite in a circular orbit?

A) Its acceleration is zero. B) Its velocity is constant. C) Its kinetic energy is constant. D) Its total energy is zero.

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

A) v_e = sqrt(GM/R) B) v_e = sqrt(2GM/R) C) v_e = GM/R D) v_e = 2GM/R

41. A satellite is orbiting the Earth in a circular orbit. If its speed is decreased by a small amount, it will:

A) Move to a higher circular orbit B) Move to a lower circular orbit C) Escape from Earth's gravity D) Stop orbiting

42. The orbital velocity of a satellite in a circular orbit of radius r is given by:

A) v_o = sqrt(GM/r) B) v_o = sqrt(2GM/r) C) v_o = GM/r D) v_o = sqrt(GM/(2r))

43. For a satellite in an elliptical orbit, the quantity that remains constant is:

A) Speed B) Kinetic energy C) Potential energy D) Angular momentum

44. If the density of a planet is increased by 8 times, keeping its radius the same, the escape velocity from its surface will:

A) Increase by 2 times B) Increase by 4 times C) Decrease by 2 times D) Remain the same

45. What is the velocity of a satellite in a circular orbit of radius r around a planet of mass M?

A) sqrt(GM/r) B) sqrt(2GM/r) C) sqrt(GM/(2r)) D) sqrt(GM*r)

46. The total energy of a satellite in an elliptical orbit is negative, which indicates:

A) It is unbound from the central body. B) It is bound to the central body. C) It is escaping from the central body. D) It is in a hyperbolic trajectory.

47. A satellite is in a circular orbit. If its kinetic energy is E, its potential energy is:

A) 2E B) -2E C) E/2 D) -E/2

48. Which of the following is a characteristic of Kepler's Third Law for satellites?

A) The square of the orbital period is proportional to the cube of the semi-major axis. B) The square of the orbital period is proportional to the square of the semi-major axis. C) The orbital period is independent of the semi-major axis. D) The square of the orbital period is inversely proportional to the cube of the semi-major axis.

49. If the distance of a satellite from the Earth is increased by 4 times, its orbital period will increase by a factor of:

A) 2 B) 4 C) 8 D) 16

50. The escape velocity formula can also be written in terms of the acceleration due to gravity (g) at the surface and the radius (R) as:

A) sqrt(gR) B) sqrt(2gR) C) sqrt(g/R) D) sqrt(2g/R)

Escape velocity and motion of satellites - Online Test

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