Two light strings, each of length `l` are fixed at points `A` and`B` on a fixed horizontal and `xy` A small are making angle `45^(@)` with the bob if the bob is displaced normal to the plane of the string and released then period of the resulting small oscillation will be

Options

A. `2 pi sqrt((2sqrt(2)l)/(g))`
B. `2pi sqrt((sqrt(2)l)/(g))`
C. `2pi sqrt((l)/(g))`
D. `2pi sqrt((1)/(sqrt(2)g))`

Answer

D

Explanation

Resulting torque on the bob` = mg'(1)/(sqrt(2)) sin theta`

`MI` of bob about axis `xy = (ml^(2))/(2)`
For small angle `theta`
`omega = sqrt((sqrt(2)g)/(1)) rArr T = 2pi sqrt((1)/(sqrt(2)g))`