A small particle of mass `m` is released from rest from point A inside a smooth hemishperical bowl as shown in figure. The ratio (X) of magnitude of centripetal force and normal reaction on the particle at any point B varies with `theta` as

Options

A.
B.
C.
D.

Answer

A

Explanation

`(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)`.