Question

A particle of mass $50\text{kg}$ thrown into the tunnel from point $\text{A}$ inside the earth, the tunnel is $d$ away from the center of the earth. A particle oscillates about a point $\text{C}$ inside the tunnel due to the gravitational force towards the centre. Calculate the time period of oscillation. (Radius of earth $=6.378\times {10}^6\text{m})$

• A. $2\text{hours}$
• B. $1.4\text{hours}$
• C. $3.5\text{hours}$
• D. $1.7\text{hours}$

Answer 1

The correct option is B $1.4\text{hours}$

We know that the time period of a particle oscillating in an arbitrary tunnel through earth is given by,

$T=2\pi \sqrt{\frac{R_E}{g}}$

$=2\pi \sqrt{\frac{6.378\times {10}^6}{9.81}}=5066.26\text{s}$

$\therefore T=1.4\text{hours}$

Hence, option $\left(\text{B}\right)$ is correct.