Answer: 1/sqrt(2).
- A 1/2
- B 1/sqrt(2)
- C sqrt(2)
- D 2
Correct answer: B. 1/sqrt(2)
Explanation: vo = sqrt(gR), ve = sqrt(2gR). Ratio vo/ve = sqrt(gR)/sqrt(2gR) = 1/sqrt(2).
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.