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  4. Two simple pendulum of lengths in the ratio 9: 1 are started at time t = 0. They will again be in phase. After shorter pendulum has made n oscillation, where n is:

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Q. Two simple pendulum of lengths in the ratio 9 : 1 are started at time t = 0. They will again be in phase. After shorter pendulum has made n oscillation, where n is:

JIPMERJIPMER 1999

Solution:

Given: The periods of pendulum are in the ratio of 3 : 1. From the relation of time period $ T\propto \sqrt{l} $ Suppose the pendulum be in phase after $ n. $ .oscillation of smaller pendulum. Then larger pendulum has made $ \left( n-1 \right) $ oscillation in the same duration it means $ \left( n-1 \right)3=n\times 1 $ Hence, $ n=\frac{3}{2} $