Two simple pandulum whose lengths are `100cm` and `121cm` are suspended side by side. Then bobs are pulled together and then released. After have minimum oscillation of the length pendulum will be two be in phase again. ?

Options

A. 11
B. 10
C. 21
D. 20

Answer

B

Explanation

Let `T_(1)` and `T_(2)` are the time period of the two pendulume
`T_(1) = 2 pi sqrt((100)/(g))` and `T_(2) = 2 pi sqrt((121)/(g))`
(`T_(1) lt T_(2)` because `T_(1) lt T_(2)`)
Let at `t = 0`, they start swinging togather since then time period are different theh swinging will not be in unision aleways. Only when number of completed oscilation difference by an integes the two perdulum will again length begain to swing togather.
Let longer length pendulum complate `n` oscillation and shorter length pendulum complete `( n + 1)` oscillation by the unison swinging, then `( n+ 1) T_(1) = nT_(2)`
`(n + 1) xx 2pi sqrt((100)/(g)) = n xx 2pi sqrt((121)/(g)) rArr n = 10`