A frictionless wire is fixed between `A` and `B` inside a circle of radius `R`. A small bead slips along the wire. Find the time taken by the bead to slip from `A` to `B`.

Options

A. `2sqrt(R//g)`
B. `gR//sqrt(g cos theta)`
C. `(2sqrt(gR))/(g cos theta)`
D. `(2sqrt(gR cos theta))/g`

Answer

A

Explanation

`AB = 2 R cos theta`
acceleration along AB
`a = g cos theta`
`u =0` from A to B

`2 R cos theta =0+(1)/(2) (g cos theta)t_(2)`
`t=2 sqrt((R)/(g))`