Answer: 4:1.
- A 2:1
- B 4:1
- C 8:1
- D 16:1
Correct answer: B. 4:1
Explanation: T<sup>2</sup> proportional to r<sup>3</sup> (Kepler). (T<sub>1</sub>/T<sub>2</sub>)<sup>2</sup> = (r<sub>1</sub>/r<sub>2</sub>)<sup>3.</sup> (8)<sup>2</sup> = (r<sub>1</sub>/r<sub>2</sub>)<sup>3.</sup> 64 = (r<sub>1</sub>/r<sub>2</sub>)<sup>3.</sup> r<sub>1</sub>/r<sub>2</sub> = 4.
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.