Question

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 upto which the particle can remain stationary is

• A. $\frac{R}{2}$
• B. $(1-\frac{\sqrt{3}}{2})R$
• C. $\frac{\sqrt{3}}{2}R$
• D. $\frac{3R}{8}$

Answer 1

The correct option is B

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

$\text{N}=\text{mg cos}\theta$

$\text{f = mg sin}\theta =\mu \times \text{N}$

$\mu =\text{tan}\theta$

$\text{tan}\theta =\frac{1}{\sqrt{3}}$

$\text{cos}\theta =\frac{R-h}{R}=\frac{\sqrt{3}}{2}$

$h=(1-\frac{\sqrt{3}}{2})\text{R}$