A uniform rod of length l is suspended by end and is made to undego small oscillations. Find the length of the simple pendulum having the time period equal to that of the rod.

Explanation

`tau=-mg1/2sintheta`
`I=(ml^2)/(3)`
`tau=-(mgl)(2)theta` (`:'sintheta=theta`)
`Ialpha=-(mgl)/(2)theta`
`alpha=-(mgl)/(2l)theta=-omega^2theta`
Time period `T=2pisqrt((2I)/(mgl))=2pisqrt((2ml^2)/(3mgl))=2pisqrt((2l)/(3g))`
Time period of simple pendulum `T^'=2pisqrt(L/g)`
`T^'=TimpliesL=(2l)/(3)`