Answer: 2*pi*sqrt((R+h) 3 /(GM)).
- A 2*pi*sqrt(R/g)
- B 2*pi*sqrt((R+h)<sup>3</sup>/(GM))
- C 2*pi*sqrt((R+h)/g)
- D 2*pi*sqrt(GM/R)
Correct answer: B. 2*pi*sqrt((R+h)<sup>3</sup>/(GM))
Explanation: T = 2*pi*sqrt(r<sup>3</sup>/(GM)) where r = R+h. Or T = 2*pi*sqrt((R+h)<sup>3</sup>/GM).
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.