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A small block of mass m is released from...

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

Text Solution

Verified by Experts

The correct Answer is:
A

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