A uniform thin hemispherical shell is kept at rest and in equilibrium on an inclined plane of angle of inclination `theta=30^(@)` as shown in figure. If the surface of the inclined plane is sufficiently rough to prevent sliding then the angle `alpha` made by the plane of hemisphere with inclined plane is :

Options

A. Value of `mu` is needed
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Explanation

O is the centre of mass of the hollow hemisphere and is R/2 from C
`f=mg sin theta.....(i)`
`N=mg cos theta.....(2)`
`NxxR/2sin alpha=[R-R/2 cos alpha] f.....(3)`
`:. tan theta=(sin alpha)/(2-cos alpha)rArr alpha=30^(@)`