A bead is free to slide down on a smooth wire rightly stretched between points `A and B` on a vertical circle of radius `10 m`. Find the time taken by the bead to reach point `B`, if the bead slides from rest from the highest point `A` on the circle.
.

Options

A. `(2sqrt(gR))/(gcostheta)`
B. `2sqrt(gR).(costheta)/(g)`
C. `2sqrt(R )/((g))`
D. `(gR)/sqrt(gcostheta)`

Answer

C

Explanation

`AB=2R cos theta`
Acceleration along `AB=g cos theta`
`AB=(1)/(2)at^(2)`
`2R cos theta=(1)/(2)gcosthetat^(2)`
`t=sqrt((4R)/(g))=2sqrt((R )/(g))`