Engineering
Physics
Question

Two equally long pendulum are hung at the same point. They are deviated by the same angle gone to the right and another to the left. If they are released simultaneously, they collide at the lowest point. One of them stops and another just completes the vertical circle. The collision is elastic. What is the mass of ball (in kg) coming to rest if the mass of other ball is 3kg.

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Solution
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mgℓℓcosθ=12mv2

v=2gℓ(1cosθ)m1v+m2v=m15gR

e=1=5gR2v

v=5gR2

m2m12=m1

m2 = 3m1 = 9 kg