Question

A hole is drilled from the surface of earth to its centre. A particle is dropped from rest at the surface of earth. The speed of the particle when it reaches the centre of the earth in terms of its escape velocity on the surface of earth $v_e$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Kinetic energy at center = potential energy at surface

- potential energy at center

or $\frac{1}{2}m{v}^2=-\frac{GMm}{R}-\left(\frac{-3}{2}\frac{GMm}{R}\right)$

or $\frac{1}{2}m{v}^2=\frac{1}{2}\frac{GMm}{R}$

or $v=\sqrt{\frac{GM}{R}}=\sqrt{gR}=\frac{v_e}{\sqrt{2}}$