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Question

Two identical simple pendulums A and B have the same point of suspension, having length each. They are displaced by an angle (α and β are very small and β>α) and released from rest. Find the time after which B reaches its initial position for the first time. Assume collision to be elastic and both pendulums move in the same plane.


A
πg
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B
2πg
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C
πβαg
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D
2πβαg
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Solution

The correct option is B 2πg
Time taken by B for first collision (i.e from angular diplacement β to mean position) =T4
Since the collision is elastic, the maximum velocities of A and B are exchanged at the mean position.

vmax=Aω where A is the amplitude and ω is the angular frequency which does not change.

Therefore, after first collision, angular displacement amplitude of B will be α.

Time taken for B to go to angular displacement α and back to mean position =T4+T4=T2
During second collision, again the maximum velocities of A and B are exchanged, so B will reach back to its initial angular displacement β in time T4+T4=T2.

So, total time taken is t=T4+T4+T4+T4=T

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