Time period of a simple pendulum of length `L` is `T_(1)` and time period of a uniform rod of the same length `L` pivoted 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. `sqrt(2)//sqrt(3)`
B. `1//sqrt(3)`
C. `sqrt(3)//sqrt(2)`
D. `1//sqrt(2)`

Answer

C

Explanation

`T_(1) = 2pi sqrt((L)/(g)) , T_(2) = 2pi sqrt((1)/(Mgd))`
`T_(2) = 2pi sqrt(((1)/(3)ML^(2))/(Mg(L)/(2))), = 2 pi sqrt((2L)/(3g))`
`(T_(1))/(T_(2)) = sqrt((3)/(2))`