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Question

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

A
11
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B
10
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C
21
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D
20
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Solution

## The correct option is B 10Let T1 and T2 be the time period of the two pendulums T1=2π√100g and T2=2π√121g (T1<T2 because l1<l2) ⇒T2T1=√121√100 ∴T2T1=1110 ⇒10T2=11T1 Hence smaller pendulum will complete one oscillation more than longer pendulum. Let longer pendulum complete n oscillations and shorter length pendulum complete (n+1) oscillations For oscillating in same phase: (n+1)T1=nT2 (n+1)×2π√100g=n×2π√121g 11n=10n+10 ∴n=10

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