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Question

Two pendulums have time period T and 5T/4. They start SHM at the same time from the mean position. What will be the phase difference between them at the moment, when bigger pendulum completes one oscillation?

A
45
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B
90
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C
60
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D
30
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Solution

The correct option is B 90
Bigger pendulum( greater (l)) will have greater time period.
Time period of smaller pendulum T1=T
Time period of bigger pendulum T2=5T4

They both start at the same time from mean position,
after time t, phase difference between them is:
Δϕ=ω1tω2t=(2πT2π5T/4)×t
when bigger pendulum completes oscillation, t=5T4
Δϕ=2π5T×5T4
Δϕ=π2
Hence, option (b) is correct

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