Answer: 3GMm/(4R).
- A GMm/(2R)
- B 3GMm/(4R)
- C 5GMm/(4R)
- D GMm/R
Correct answer: B. 3GMm/(4R)
Explanation: E<sub>surface</sub> = -GMm/R. E<sub>orbit</sub>(2R) = -GMm/4R. Delta E = -GMm/4R - (-GMm/R) = GMm(1/R - 1/4R) = 3GMm/(4R).
g is maximum at Earth's surface; going up, it falls off as 1/r² (inverse-square); going down, it falls off linearly with depth (since only the mass enclosed within radius r contributes), reaching zero at the centre.
Concept context
Universal gravitation, orbital mechanics, gravitational potential, and escape velocity.