A partical is placed at rest inside a hollow hemisphare of redius `R`. The coefficient of friction between the partical and the homisphere is `mu = (1)/sqrt(3)`. The maximum height up to which the partical can remain stationary is

Options

A. `(R )/(2)`
B. `(1 - sqrt(3)/(2)) R`
C. `sqrt(3)/(2) R`
D. `(3 R)/(8)`

Answer

B

Explanation

Angle of repose `theta = tan ^(-1) (mu)`
`= tan ^(-1) ((1)/sqrt(3)) = 30^(@)`

So, particle may be placed maximum upto `30^(@)`, as shown in figure
`h = R - R cos 30^(@) = (1 - sqrt(3)/(2)) R`