Question

A diametrical tunnel is dug across the Earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reaches the centre of the Earth is.....(Given: gravitational potential at the centre of Earth $=-\frac{3}{2}\frac{GM}{R}$)

• A. $\sqrt{R}$
• B. $\sqrt{gR}$
• C. $\sqrt{2.5gR}$
• D. $\sqrt{7.1gR}$

Answer 1

Answer: (B)

$\sqrt{gR}$

Loss in potential energy = Gain in kinetic energy
$-\frac{GMm}{R}-(-\frac{3}{2}\frac{GMm}{R})=\frac{1}{2}m{v}^2$
$\Rightarrow \frac{GMm}{2R}=\frac{1}{2}m{v}^2\Rightarrow v=\sqrt{\frac{GM}{R}}=\sqrt{gR}$