Time period of a simple pendulum of length 'L' is `T_(1)` . Time period of a uniform rod of same length 'L' suspended from one end and oscillating in a vertical plane is `T_(2)` . Amplitude of oscillation is small in both the cases . Them `(T_(1))/(T_(2))` is

Options

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

Answer

B

Explanation

Given,
Length of pendulum = L
Time period `T_(1) = 2 pi sqrt((L)/(g))`
Length of rod = L
Time period of rod:
`T_(2) = 2 pi sqrt((2L)/(3g))`
`(T_(1))/(T_(2)) = (2pi sqrt(L//g))/(2pi sqrt(2L //3g))`
`= sqrt((3)/(2))`