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

Answer

C

Explanation

Acceleration along AB is g`cos theta`
`a = g cos theta`
`S_(AB) = 1/2 a t^2 = 1/2 (g cos theta) t^2`
From `Delta ABC, AC cos theta = AB rArr AB = 2R cos theta`
`2R cos theta = 1/2 g cos theta t^2 rArr (4R)/(g) = t^2`
`rArr t = 2 sqrt(R/g)`