Two pendulums at rest swinging together. Their lengths are respectively `1.44 m` and `1 m`. They will again start swinging in same phase together after (of longer pendulum) :

Options

A. `1` vibration
B. `3` vibrations
C. `4` vibrations
D. `5` vibrations

Answer

D

Explanation

Let `x_(1) = A_(1)sinomega_(1)t` and `x_(2) = A_(2)sinomega_(2)t`
Two pendulums will vibrate in same phase again when there phase difference `(omega_(2) - omega_(1))t = 2pi`
`rArr ((2pi)/(T_(2)) - (2pi)/(T_(1)))t = 2pi`
`rArr (sqrt((g)/(1)) - sqrt((g)/(1.44)))n xx T_(1) = 2pi` (where `n` is number of vibrations completed by ionger pendulum)
`rArr (sqrt((g)/(1)) - sqrt((g)/(1.44)))n xx 2pisqrt((1.44)/(g)) = 2pi rArr n = 5`
Thus after `5` vibrations of longer pendulum they will again start swinging in same phase.