Answer: ve*sqrt(6)/4.
- A ve/sqrt(24)
- B ve*sqrt(6)/4
- C ve/sqrt(6)
- D ve/4
Correct answer: B. ve*sqrt(6)/4
Explanation: ve_moon = sqrt(2 x g<sub>moon</sub> x R<sub>moon</sub>) = sqrt(2 x g/6 x R/4) = sqrt(gR/12) = ve x sqrt(1/24) = ve/sqrt(24). Hmm. ve = sqrt(2gR). ve_moon = sqrt(2(g/6)(R/4)) = sqrt(gR/12) = sqrt(gR)/sqrt(12). ve_moon/ve = sqrt(1/12)/sqrt(2) = 1/sqrt(24). So ve_moon = ve/sqrt(24).
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.