Problem

A particle is placed at rest inside a hollow hemisphere of radius

R

. The coefficient of friction between the particle and the hemisphere is

\mu = \frac{1}{\sqrt{3}}

. The maximum height up to which the particle can remain stationary is a.

\frac{R}{2}

\left(1 - \frac{\sqrt{3}}{2}\right)R

\frac{\sqrt{3}}{2}R

\frac{3R}{8}