Question

A particle rests on the top of a hemisphere of radius $R$. Find the smallest horizontal velocity that must be imparted to the particle, if it is to leave the hemisphere without sliding down it.

• A. $\sqrt{gR}$
• B. $\sqrt{2gR}$
• C. $\sqrt{3gR}$
• D. $\sqrt{5gR}$

Answer 1

The correct option is A $\sqrt{gR}$

The smallest horizontal velocity
$v^2=gR$
where $R$ is the radius of hemisphere
$\Rightarrow$ $v=\sqrt{gR}$