Answer: 2*sqrt(2):3*sqrt(3).
- A 2:3, treating the period as directly proportional to radius
- B 4:9, treating the period as proportional to the square of radius
- C 2*sqrt(2):3*sqrt(3)
- D 8:27, treating the period as proportional to the cube of radius
Correct answer: C. 2*sqrt(2):3*sqrt(3)
Explanation: T proportional to r<sup>3/2</sup>. T<sub>1</sub>:T<sub>2</sub> = (2R)<sup>3/2</sup> : (3R)<sup>3/2</sup> = 2*sqrt(2) : 3*sqrt(3).
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.