Question

A tunnel is dug along the diameter of the earth. A mass $m$ is dropped into it. How much time does it take to cross the earth?

• A. $169.2minutes$
• B. $84.6minutes$
• C. $21.2minutes$
• D. $42.3minutes$

Answer 1

Answer: (D)

$42.3minutes$

The mass will execute SHM in the tunnel.

Time period of oscillation $T=2\pi \sqrt{\frac{R}{g}}$

where $R=6.4\times {10}^{6}m$ and $g=9.8m/s^2$

$⟹T=2\pi \sqrt{\frac{6.4\times {10}^6}{9.8}}s=5075s$

So we get $T=\frac{5075}{60}=84.6minutes$

Time taken to cross the tunnel $t=\frac{T}{2}=\frac{84.6}{2}=42.3minutes$