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Two simple pendulum whose lengths are 10...

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

A

11

B

10

C

21

D

20

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Let `T_(1)` and `T_(2)` be the time period of the two pendulums
`T_(1)=2pisqrt((100)/(g))` and `T_(2)=2pisqrt((121)/(g)) " "(T_(1) lt T_(2) "because" l_(1) lt l_(2))`
Let at t=0 , they start swinging together. Since their time periods are different , the swinging will not be in unision always. Only when number of completed oscillation differs by an integer, the two pendulum will again begin to swing together.
Let longer length pendulum complete n oscillation and shorter length pendulum complete (n+1) oscillation, for the unision swinging, then `(n+1)T_(1)=nT_(2)`.
`(n+1)xx 2pisqrt((100)/(g))=nxx 2pisqrt((121)/(g))impliesn=10`
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