1. What is the value of g at a height above Earth’s surface that is equal to the radius of Earth?

(A) 9.8 N/kg
(B) 4.9 N/kg
(C) 6.93 N/kg
(D) 2.45 N/kg

2. A planet has half the mass of Earth and half the radius. Compared to the acceleration due to gravity near the surface of Earth, the acceleration of gravity near the surface of this other planet is

(A) twice as much
(B) one-fourth as much
(C) half as much
(D) the same

3. Which of the following is an expression for the acceleration of gravity at the surface of a planet with uniform density ρ and radius r?

(A) G(4πρ/3r²)
(B) G(4πρr²/3)
(C) G(4πρ/3r)
(D) G(4πrρ/3)

4. What is the orbital velocity of a satellite at a height of 300 km above the surface of Earth? (The mass of Earth is approximately 6 × 10²⁴ kg, and its radius is 6.4 × 10⁶ m.)

(A) 5.42 × 10¹ m/s
(B) 1.15 × 10⁶ m/s
(C) 7.7 × 10³ m/s
(D) 6 × 10⁶ m/s

5. What is the escape velocity from the Moon, given that the mass of the Moon is 7.2 × 10²² kg and its radius is 1.778 × 10⁶ m?

(A) 1.64 × 10³ m/s
(B) 2.32 × 10³ m/s
(C) 2.69 × 10⁶ m/s
(D) 5.38 × 10⁶ m/s

6. A black hole theoretically has an escape velocity that is greater than or equal to the velocity of light (3 × 10⁸ m/s). If the effective mass of the black hole is equal to the mass of the Sun (2 × 10³⁰ kg), what is the effective “radius” (called the “Schwarzschild radius”) of the black hole?

(A) 3 × 10³ m
(B) 1.5 × 10³ m
(C) 8.9 × 10⁶ m
(D) 4.45 × 10⁶ m

7. What is the gravitational force of attraction between two trucks, each of mass 20,000 kg, separated by a distance of 2 m?

(A) 0.057 N
(B) 0.013 N
(C) 0.0067 N
(D) 1.20 N

8. The gravitational force between two masses is 36 N. If the distance between masses is tripled, the force of gravity will be

(A) the same
(B) 18 N
(C) 9 N
(D) 4 N

1. Find the magnitude of the gravitational field strength g at a point P along the perpendicular bisector between two equal masses, M and M, that are separated by a distance 2b as shown below:

2. Explain why a heavier object near the surface of Earth does not fall faster than a lighter object (Neglect air resistance).

3. Show that the units for g in N/kg are equivalent to m/s². Why is g referred to as the “gravitational field strength”?

4. Explain why objects in orbit appear to be “weightless.”

5. Find the orbital radius for a geosynchronous satellite. A geosynchronous satellite is a satellite around Earth that is synchronized, in that its orbital period is 24 hours, just like Earth itself. The mass of Earth is approximately 6.0 × 10²⁴ kg.