Answer: GMm/(4R).
- A GMm/(4R)
- B GMm/(2R)
- C 3GMm/(4R)
- D GMm/R
Correct answer: A. GMm/(4R)
Explanation: Surface total energy = -GMm/R. Orbital total energy at 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.