Engineering
Physics
Collision
Question

A bullet of mass m and velocity v passes through a pendulum bob of mass M and emerges with velocity v/2 (figure). The pendulum bob is at the end of a string of length ℓ. What is the minimum value of v (in m/s) such that the pendulum bob will swing through a complete circle ? (Take : ℓ = 2m, M = 1kg, m = 10 gm.)

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Solution
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mv = Mv1 + M v/2

v1=mv2M=5gℓ

v=2Mm5gℓ

v=2Mm5gℓ=2×10.01100=2000m/s

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