Escape velocity and motion of satellites - Question Bank

1. 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)
2. 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
3. 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.
4. 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
5. 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.
6. 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)
7. 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
8. For a satellite in an elliptical orbit, the quantity that remains constant is:
A) Speed
B) Kinetic energy
C) Potential energy
D) Angular momentum
9. 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))
10. 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
11. 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
12. 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.
13. 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
14. 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
15. 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.
16. 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
17. 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
18. 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
19. 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.
20. 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
21. 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
22. 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)
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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)
31. 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))
32. What is the unit of escape velocity?
A) m/s^2
B) m/s
C) Joule
D) kg/m^3
33. 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
34. 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
35. 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.
36. 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
37. 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)
38. 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)
39. 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
40. A geostationary satellite orbits the Earth at a height of approximately:
A) 100 km
B) 1000 km
C) 36000 km
D) 100000 km
41. For a geostationary satellite, its time period of revolution is:
A) 6 hours
B) 12 hours
C) 24 hours
D) 48 hours
42. 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)
43. 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
44. 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)
45. 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)
46. 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
47. 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
48. 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
49. 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
50. 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
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