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 is

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

Answer 1

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

The velocity should be such that the centripetal acceleration is equal to the acceleration due to gravity
$\Rightarrow \frac{v^2}{R}=g$
or, $v=\sqrt{Rg}$