A bead of mass m is released from rest at A to move along the fixed smooth circular track as shown in figure. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point `P_0` described by the angle `theta(!=0)` would

Options

A. (a) Increase with `theta`
B. (b) Decrease with `theta`
C. (c) Remain constant
D. (d) First increase with `theta` and then decrease

Answer

C

Explanation

Conservation of energy gives
`1/2mv^2=mgRsinthetaimplies(mv^2)/(R)=2mgsintheta=F_C`
Now, `N-mg sin theta=F_CimpliesN=3mg sin theta`
`:. F_C/N=2/3`