Question

A small block of mass `m` is released from rest from point `A` inside a smooth hemisphere bowl of radius `R`, which is fixed on group such that `OA` is horizontal. The ratio `(x)` of magnitude of centripetal force and normal reaction on the block at any point `B` varies with `theta` as :

A.
B.
C.
D.

Answer 1

Correct Answer - A
`(mv^(2))/(R)=N-mgsintheta`

`N=(mv^(2))/(R)+mgsin theta`
By energy conservation,
`mgR sin theta =(1)/(2) mv^(2)`
`(mv^(2))/(R)=3mg sin theta`
`N= 3mgsin theta`
Ratio `=(mv^(2))/(RN)=(2)/(3)(` constant `)`
`x=(2)/(3)`.