Question

The escape velocity from a planet is $V_e$. A tunnel is dug along a diameter of the planet and a small body is dropped into it. The time taken by the body to reach the centre of the planet will be

• A. $\frac{\pi }{2}\sqrt{\frac{R}{g}}$
• B. $\pi \sqrt{\frac{R}{g}}$
• C. $2\pi \sqrt{\frac{R}{g}}$
• D. $\sqrt{\frac{R}{g}}$

Answer 1

The correct option is A $\frac{\pi }{2}\sqrt{\frac{R}{g}}$

Time period of oscillation of the particle in the tunnel,
$T=2\pi \sqrt{\frac{R}{g}}$
The journey from surface to the centre is one fourth of an oscillation.
$=$ time taken by body $=\frac{T}{4}=\frac{\pi }{2}\sqrt{\frac{R}{g}}$
Option A.