Question

A small disc is placed at the top of a hemisphere of radius R as shown in figure. What is the smallest velocity that should be given to the disc for it to leave the hemisphere and not slide down it?

• A. $v=\sqrt{2gR}$
• B. $v=\sqrt{gR}$
• C. $v=2\sqrt{gR}$
• D. $v=\sqrt{\frac{gR}{2}}$

Answer 1

The correct option is B $v=\sqrt{gR}$

Weight of disc = mg, this provides the necessary centripetal force
$mg=\frac{m{v}^2}{R}v=\sqrt{gR}$