Keplers laws of planetary motion, gravitational potential energy and gravitational potential - Question Bank

1. What is the relationship between gravitational potential energy (U) and gravitational force (F) for a system of two masses?
A) F = -dU/dr
B) F = dU/dr
C) F = U/r
D) F = -U/r
2. The work done in moving a particle of mass 'm' from a point A to a point B in a gravitational field is independent of the path taken if the gravitational force is:
A) Non-conservative
B) Conservative
C) Uniform
D) Variable
3. According to Kepler's Third Law, for planets orbiting the Sun, the ratio T^2/a^3 is:
A) Different for each planet
B) The same for all planets
C) Proportional to the mass of the planet
D) Inversely proportional to the mass of the planet
4. The gravitational potential at a point is the potential energy per unit:
A) Mass
B) Volume
C) Charge
D) Area
5. If we define the gravitational potential energy of an object to be zero at the Earth's surface, then at a height 'h' above the surface, it would be:
A) mgh
B) -mgh
C) GMm/h
D) -GMm/h
6. The gravitational potential energy of a satellite of mass 'm' in a circular orbit of radius 'r' around the Earth of mass 'M' is:
A) -GMm/r
B) GMm/r
C) -GMm/(2r)
D) GMm/(2r)
7. Which law states that the line joining a planet and the Sun sweeps out equal areas in equal intervals of time?
A) Kepler's First Law
B) Kepler's Second Law
C) Kepler's Third Law
D) Newton's Law of Gravitation
8. The gravitational potential energy of a system of two identical masses 'm' separated by a distance 'r' is:
A) Gm^2/r
B) -Gm^2/r
C) 2Gm^2/r
D) -2Gm^2/r
9. Kepler's Third Law is often used to determine the mass of a central body if the orbital parameters of a satellite are known. If a satellite's period is T and its orbital radius is R (for a circular orbit), the mass of the central body is proportional to:
A) T^2 / R
B) R^2 / T
C) R^3 / T^2
D) T^2 / R^3
10. If the Earth's mass is doubled and its radius is halved, what happens to the gravitational potential at its surface?
A) It remains the same
B) It becomes half
C) It becomes four times
D) It becomes twice
11. The gravitational potential at a distance 'r' from a point mass 'M' is numerically equal to the work done per unit mass in bringing the mass from infinity to that point. This work done is:
A) Positive
B) Negative
C) Zero
D) Depends on the sign of M
12. For a planet in an elliptical orbit, the speed is highest when it is:
A) Farthest from the Sun
B) Closest to the Sun
C) At the end of the semi-minor axis
D) At the center of the ellipse
13. The gravitational potential energy of a system of two particles of masses m1 and m2 at infinite separation is defined as:
A) G m1 m2 / ∞
B) -G m1 m2 / ∞
C) 0
D) Undefined
14. Kepler's First Law is a specific case of which mathematical conic section?
A) Circle
B) Parabola
C) Hyperbola
D) Ellipse
15. The gravitational potential at a point P is V. If a mass 'm' is brought from infinity to P, the work done by the gravitational field is:
A) mV
B) -mV
C) m/V
D) -m/V
16. Which planet has the shortest orbital period around the Sun?
A) Earth
B) Mars
C) Mercury
D) Venus
17. If the Sun suddenly vanished, the gravitational potential energy of the Earth would become:
A) Zero
B) Infinite
C) Negative infinity
D) Undefined
18. The gravitational potential energy of an object of mass 'm' at a height 'h' above the Earth's surface (mass M, radius R) is approximately:
A) mgh
B) -GMm/R
C) -GMm/(R+h)
D) -GMm/h
19. Kepler's Second Law is a consequence of the conservation of:
A) Energy
B) Linear momentum
C) Angular momentum
D) Mass
20. If the distance between two masses is doubled, their gravitational potential energy:
A) Is doubled
B) Is halved
C) Becomes one-fourth
D) Becomes one-half
21. What is the gravitational potential at the center of a uniform solid sphere of mass M and radius R?
A) -3GM/(2R)
B) -GM/R
C) -GM/(2R)
D) 0
22. The work done by the gravitational force as a planet moves from perihelion to aphelion in its orbit is:
A) Positive
B) Negative
C) Zero
D) Depends on the shape of the ellipse
23. According to Kepler's First Law, the eccentricity 'e' of a circular orbit is:
A) e = 0
B) 0 < e < 1
C) e = 1
D) e > 1
24. The gravitational potential energy of a system of N particles is the sum of the potential energies of all possible pairs of particles. For a system of three particles, it is:
A) U12 + U23 + U31
B) U12 + U23
C) U12
D) U1 + U2 + U3
25. Gravitational potential is a scalar quantity, while gravitational field is a vector quantity. The relationship between them is:
A) Field = -Gradient of Potential
B) Field = Gradient of Potential
C) Field = Integral of Potential
D) Field = Potential / Distance
26. If the Earth were to collapse to a point mass, its gravitational potential at its surface would:
A) Increase
B) Decrease
C) Remain the same
D) Become zero
27. Consider a planet moving in an elliptical orbit around the Sun. Its angular momentum is conserved because:
A) The gravitational force is conservative
B) The gravitational force is a central force
C) The planet's mass is constant
D) The Sun's mass is much larger than the planet's mass
28. Kepler's Third Law relates the orbital period (T) and the semi-major axis (a) of an elliptical orbit for planets around the same star. For two planets 1 and 2, the ratio of their periods squared is equal to:
A) (T1/T2)^2 = (a2/a1)^3
B) (T1/T2)^2 = (a1/a2)^3
C) (T1/T2)^3 = (a1/a2)^2
D) (T1/T2)^3 = (a2/a1)^2
29. The gravitational potential energy of a system of particles is defined as the work done by an external agent against the gravitational force to assemble the system from a configuration where the potential energy is zero. This zero potential energy configuration is typically:
A) When the particles are in contact
B) When the particles are at infinite separation
C) When the particles are at their closest approach
D) When the particles are in stable equilibrium
30. The work done to bring a unit positive test mass from infinity to a point in a gravitational field is equal to:
A) The gravitational field strength at that point
B) The negative of the gravitational field strength at that point
C) The gravitational potential at that point
D) The negative of the gravitational potential at that point
31. If the semi-major axis of a planet's orbit is doubled, how does its orbital period change according to Kepler's Third Law?
A) It doubles
B) It becomes four times larger
C) It becomes approximately 2.8 times larger (2^1.5)
D) It remains the same
32. The gravitational potential due to a point mass 'M' at a distance 'r' is given by:
A) GM/r
B) -GM/r
C) GM/r^2
D) -GM/r^2
33. Which of the following is NOT a direct consequence of Kepler's laws?
A) Planetary orbits are elliptical
B) Planets sweep equal areas in equal times
C) The force causing planetary motion is attractive
D) The square of the period is proportional to the cube of the semi-major axis
34. What is the gravitational potential at infinity?
A) Positive infinity
B) Negative infinity
C) Zero
D) Undefined
35. The gravitational potential energy of a system is the energy stored in the system due to:
A) The motion of the objects
B) The positions of the objects
C) The temperature of the objects
D) The charge of the objects
36. The 'areal velocity' of a planet, as described by Kepler's Second Law, is:
A) Equal to its linear velocity
B) Constant
C) Inversely proportional to its distance from the Sun
D) Directly proportional to its distance from the Sun
37. If a planet has a larger semi-major axis, its orbital period will be:
A) Shorter
B) Longer
C) The same
D) Unpredictable
38. The gravitational potential at the center of a uniform spherical shell of mass M and radius R is:
A) -GM/R
B) 0
C) -GM/(2R)
D) GM/R
39. The gravitational potential energy of a satellite in orbit around the Earth is:
A) Always positive
B) Always negative
C) Zero
D) Can be positive or negative depending on the orbit
40. What is the unit of gravitational potential?
A) Joule/kg
B) Newton/kg
C) Joule
D) Newton
41. If a body of mass 'm' is moved from infinity to a point at distance 'r' from a mass 'M', the change in its gravitational potential energy is:
A) GMm/r
B) -GMm/r
C) GMm*r
D) -GMm*r
42. The gravitational potential at the surface of the Earth (mass M, radius R) is:
A) GM/R
B) -GM/R
C) GM/R^2
D) -GM/R^2
43. Gravitational potential at a point is defined as the work done per unit:
A) Mass in bringing a unit mass from infinity to that point
B) Mass in moving a unit mass from that point to infinity
C) Volume in bringing a unit mass from infinity to that point
D) Charge in bringing a unit charge from infinity to that point
44. The gravitational potential energy is taken to be zero when the separation between the masses is:
A) Zero
B) Infinite
C) Equal to the radius of the larger mass
D) Equal to the radius of the smaller mass
45. Gravitational potential energy of a system of two point masses m1 and m2 separated by a distance r is given by:
A) G * m1 * m2 / r
B) -G * m1 * m2 / r
C) G * m1 * m2 * r
D) -G * m1 * m2 * r
46. For a planet orbiting the Sun, the quantity that remains constant according to Kepler's Second Law is:
A) Angular momentum
B) Linear momentum
C) Kinetic energy
D) Potential energy
47. If T is the orbital period and R is the radius of a circular orbit (approximating semi-major axis), Kepler's Third Law can be expressed as:
A) T ∝ R
B) T ∝ R^2
C) T^2 ∝ R^3
D) T^3 ∝ R^2
48. The path of a planet around the Sun is an ellipse, with the Sun at one of the foci. This is a statement of:
A) Kepler's First Law
B) Kepler's Second Law
C) Kepler's Third Law
D) Newton's Law of Gravitation
49. Kepler's Second Law implies that a planet's orbital speed is:
A) Constant throughout its orbit
B) Maximum when it is farthest from the Sun
C) Minimum when it is closest to the Sun
D) Not constant, varying such that the line joining the planet to the Sun sweeps out equal areas in equal intervals of time
50. Which of Kepler's laws states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit?
A) Kepler's First Law (Law of Ellipses)
B) Kepler's Second Law (Law of Areas)
C) Kepler's Third Law (Law of Periods)
D) Newton's Law of Universal Gravitation