Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately) (take , radius of earth )
- (A)24 hours
- (B)1 hour 24 minutes✓ Correct
- (C)1 hour 40 minutes
- (D)12 hours
Answer: (B)
Solution
A particle released in a tunnel through a uniform earth feels a restoring acceleration , which is simple harmonic with . Its period is . This equals about minutes, so the motion repeats in roughly hour minutes.
JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option