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

Answer

D

Explanation

Resulting torque on the bob `= "mg" (l)/(sqrt(2)) sin theta`
Ml of bob about axis `xy = (ml^(2))/(2)`
For small angle `theta = "mg" (l)/(sqrt(2)) sin theta`
`alpha = (tau)/(I) = (sqrt(2) g)/(l) theta`

`omega=sqrt((sqrt(2)g)/(k))rArr T=2pi sqrt((l)/(sqrt(2)g))`.