Time period of is simple pendulum of length `L` is `T_(1)` and the point time peirod of a uniform rod of the same length `L` pivotal about one end and oscillating in vertical plane is `T_(2)`. Amplitude of oscillation in both the cased is small. The `T_(1)//T_(2)` is:

Options

A. `(1)/(sqrt3)`
B. `1`
C. `sqrt(4/3)`
D. `sqrt(3/2)`

Answer

D

Explanation

`T_1=2pisqrt(l/g)`

`tau=-mg1/2sintheta`
`Ialpha=(ml^2)/(3)alpha=-mgl/2theta` (`:' sin theta=theta`)
`alpha=-(3g)/(2l)theta=-omega^2theta`
`T_2=2pisqrt((2l)/(3g))`
`T_1/T_2=sqrt(3/2)`