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. $169.2 \, min$
• B. $84.6 \, min$
• C. $21.2 \, min$
• D. $42.3 \, min$

Answer 1

Answer: (D)

Time period to cross the earth once along its diameter $=\frac{T}{2}$
$=\frac{1}{2}\left(2 \pi \sqrt{\frac{R}{g}}\right)$
$=\pi \sqrt{\frac{R}{g}}$
Where, $R$ is the radius of the earth
$=3.14\times \sqrt{\frac{6.4 \times 10^{6}}{9.8}}=2537.5 \, s$
$=42.3 \, min$