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

Options

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

Answer

C

Explanation

If `t` is the line taken by pendulum to come in same phase angle line after `t = 0`
and `N_(s)= `number of oscilation made by short length pendulum with line period `T_(2)`
Then `t = N_(s)T_(s) = N_(1)T_(1)`
`rArrr N_(s) 2pi sqrt((5)/(g)) = N_(2) xx 2 pi sqrt((20)/(g)) (:' T = 2 pi sqrt((1)/(g))`
`rArr N_(s) = 2N_(1)` i.e. if `N_(2) = 1 rArr N_(s) = 2`