A system of two identical rods (L-shaped) of mass `m` and length `l` are resting on a peg `P` as shown in the figure. If the system is displaced in its plane by a small angle `theta`,find the period of oscillations:

Options

A. `2pisqrt((sqrt2l)/(3g))`
B. `2pisqrt((2sqrt2l)/(3g))`
C. `2pisqrt((2l)/(3g))`
D. `3pisqrt((l)/(3g))`

Answer

C

Explanation

`T=2pisqrt((I)/(mgL))`
here `I=(ml^2)/(3)+(ml^2)/(3)=(2mgl^2)/(3)`
From figure, `sin45^@=(L)/((l)/(2))`
`L=(l)/(2sqrt2)` `t=2pisqrt((2ml^2)/(3xx(l)/(2sqrt3)mg))=sqrt((2sqrt2l)/(3g))`