Two simple pendulum of length `5m` and `20m` respectively are given small displacement in one direction at the same time. They will again be in the same phase when the pendulum of shorter length has completed oscillation.

Options

A. 5
B. 1
C. 2
D. 3

Answer

A

Explanation

Let `T_(1) and T_(2)` be the time period of shorter length and longer length pendulums reapectively. As per question, `nT_(1) = (n-1)T_(2)`
So, `n 2 pi sqrt((0.5)/(g))=(n-1)2 pi sqrt((20)/(g))`
or `n = (n-1)sqrt(40)=(n-1)6`
Hence, 5n = 6
Hence, after 5 oscillations they will be in same phase.