Question

A straight tunnel is dug into the earth as shown in figure at a distance $b$ from its centre. A ball of mass $m$ is dropped from one of its ends. The time it takes to reach the other end is approximately

• A. $42\text{min}$
• B. $84\text{min}$
• C. $\left(\frac{84b}{R}\right)\text{min}$
• D. $\left(\frac{42b}{R}\right)\text{min}$

Answer 1

The correct option is A $42\text{min}$

Time period is given by,

$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{R}{g}}$

Substituting, $R=64\times {10}^5\text{m}$ and $g=10{\text{m/s}}^2$, we get

$\Rightarrow T=2\pi \sqrt{\frac{64\times {10}^5}{10}}$

$\Rightarrow T=1600\pi \text{sec}$

$\Rightarrow T=\frac{1600\pi }{60}=83.8\text{min}$

So, time taken by ball from one end to other end is $T/2=41.9\text{min}$.

Hence, option (a) is correct answer.