A particle is placed at rest inside a hollow hemisphere of radius R. The coefficient of friction between the particle and the hemisphere is $\mathrm{\mu }=\frac{1}{\sqrt{3}}$. The maximum height up to which the particle can remain stationary is

• A

  $\frac{\mathrm{R}}{2}$

• B

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

• C

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

• D

  $\frac{3\mathrm{R}}{8}$