Center of Mass, Momentum & Collision

JEE Main level, numerical answer, medium

16 of 130

Question 16 of 130

A bullet of 10g10g, moving with velocity vv, collides head-on with the stationary bob of a pendulum and recoils with velocity 100ms−1100m{s}^{-1}. The length of the pendulum is 0.5m0.5m and mass of the bob is 1kg1kg. The minimum value of vinms−1v\text{in}m{s}^{-1}, so that the pendulum describes a circle. (Assume the string to be inextensible and g=10ms−2g=10m{s}^{-2} )

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Answer: 400

Final velocity of system (bullet ++ mass) should be =5gr=\sqrt{5gr}
Now M5gr=m(v+100)M\sqrt{5gr}=m(v+100)
thus v=Mm5gr−100=500−100=400ms−1v=\dfrac{M}{m}\sqrt{5gr}-100=500-100=400m{s}^{-1}
v=400ms−1v=400m{s}^{-1}

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