A friction wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by the ball to slip from A to B.

Options

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

Answer

C

Explanation

Acceleration of the body along `AB = g cos theta`
Distance travelled in time
`t sec = AB = 1/2 (g cos theta)t^(2)`
From `DeltaABC`
`AB = 2R cos theta`
or `1/2 (gcostheta)t^(2) = 2R cos theta`
or `1/2 (g cos theta)t^(2) = 2R cos theta`
`:. t = 2 sqrt((R)/(g))`