Two pendulum of different angle are in pgase at mean position at a cartain The minimum and after which they will be again in phase is `5T//4` where in the period of shaorter pendulum find the ratio length of the two pendulum

Options

A. `1:16`
B. `1:4`
C. `1:2`
D. `1:25`

Answer

D

Explanation

Let `T_(1) = T and T_(2) = KT,(2pi)/(T) t - (2pi)/(KT) t = 2pi`
`t((K - 1)/(KT)) = 1, ((K - 1)/(KT)) = 1 which given K = 5`
If length of first pendulum `= t, T_(1) = 2pi sqrt(1//g)`
`T_(2) = 5 xx sqrt(1//g) = 2pi sqrt(25//g)`
So ratio of length `= 1: 25`