A particle of mass `m` initially at rest starts moving from point `A` on the surface of a fixed smooth hemisphere of radius `r` as shown. The particle looses its contact with hemisphere at point `B.C` is centre of the hemisphere. The equation relating `theta` and `theta'` is
.

Options

A. `3 sin theta = 2 cos theta'`
B. `2 sin theta = 3 cos theta'`
C. `3 sin theta' = 2 cos theta`
D. `2 sin theta = 3 cos theta'`

Answer

C

Explanation

Let `v` be the speed of particle at `B` when it is about to loose contact `(mv^(2))/( r) = mg sin theta'`
Applying conservation of energy
`(1)/(2) mv^(2) = mg (r cos theta - r sin theta')`
`3 sin theta' = 2 cos theta`.