Question

A particle rests on the top of a hemisphere of radius, $R$. The minimum linear horizontal velocity for the particle to leave the vertex without slipping will be

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

Answer 1

Answer: (C)

$v=\sqrt{gR}$

$mg-N=\frac{m{v}^2}{R}$
To leave the surface, $N=0$
$\Rightarrow mg=\frac{m{v}^2}{R}\Rightarrow v=\sqrt{gR}$