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Q.

Two pendulums 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 5T/4, where T is the time period of shorter pendulum. Find the ratios of lengths of the two Pendulums.

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a

1:16

b

1:4

c

1:2

d

1:25

answer is D.

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Detailed Solution

Let T1=T and T2=KT;2πTt−2πKTt=2πtK−1KT=1;5T4K−1KT=1 which gives K=5 If length of first pendulum =l,T1=2πl/gT2=5×2πl/g=2π25l/g So, ratio of lengths =1:25.

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Two pendulums 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 5T/4, where T is the time period of shorter pendulum. Find the ratios of lengths of the two Pendulums.