Answer: -GMm/(2r).
- A -GMm/r
- B -GMm/(2r)
- C GMm/(2r)
- D GMm/r
Correct answer: B. -GMm/(2r)
Explanation: KE = GMm/(2r), PE = -GMm/r. Total E = KE+PE = GMm/(2r) - GMm/r = -GMm/(2r). (Negative means bound system.)
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.