Answer: ve = sqrt(2) x vo.
- A ve = vo
- B ve = 2vo
- C ve = sqrt(2) x vo
- D vo = sqrt(2) x ve
Correct answer: C. ve = sqrt(2) x vo
Explanation: vo = sqrt(gR), ve = sqrt(2gR) = sqrt(2) x vo. Escape velocity is sqrt(2) times orbital velocity.
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.