Q.

Two pendulum of different lengths are in phase at the mean position at a certain instant. The minimum time after which they will be again in phase is 5T4, where T is the time period of shorter pendulum. Find the ratio of lengths of the two pendulums.

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a

1 : 16

b

1 : 4

c

1 : 2

d

1 : 25

answer is .

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Detailed Solution

Let T1 = T and T2 = KT, 2πTt-2πKTt = 2πt(K-1KT) = 1; 5T4(K-1KT) =1 which gives K =5If length of first pendulum = l, T1 = 2πlgT2 = 5 ×2πlg = 2π25lgSo, ratio of lengths = 1 : 25
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Two pendulum of different lengths are in phase at the mean position at a certain instant. The minimum time after which they will be again in phase is 5T4, where T is the time period of shorter pendulum. Find the ratio of lengths of the two pendulums.