Question

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 $g=10 \, m s ^{-2}$, radius of earth $=6400 \,km$ )

• A. 1 hour 24 minutes
• B. 1 hour 40 minutes
• C. 12 hours
• D. 24 hours

Answer 1

Answer: (A)

1 hour 24 minutes

Answer 2

Let at some time particle is at a distance x from centre of Earth, then at that position field
E=R3xGM​
∴ Acceleration of particle
a=−R3GM​x
⇒ω=R3GM​​=Rg​​
Now T=ω2π​=2πgR​​
⇒T=2×3.14×106400×103​​
=2×3.14×800sec≈1 hour 24 minutes