Answer: sqrt(gR/2).
- A sqrt(gR/2)
- B sqrt(gR)
- C sqrt(2gR)
- D sqrt(gR/4)
Correct answer: A. sqrt(gR/2)
Explanation: vo = sqrt(GM/(2R)). GM = gR<sup>2.</sup> vo = sqrt(gR<sup>2</sup>/(2R)) = sqrt(gR/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.