Question

A mass $m$ slips along the wall of a spherical surface of radius $R$. The velocity at the bottom of the surface is:

• A. $\sqrt{Rg}$
• B. $\sqrt{2Rg}$
• C. $2\sqrt{\pi Rg}$
• D. $\sqrt{\pi Rg}$

Answer 1

The correct option is B $\sqrt{2Rg}$

Height difference from bottom to top is $R$

From conservation of energy,

Kinetic energy is equal to potential energy.

$\frac{1}{2}m{v}^2=mgR$

$v=\sqrt{2gR}$

Hence, velocity at bottom is $\sqrt{2gR}$