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Question

A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass 10−2kg moving with a speed of 2×102ms−1. The height to which the bob rises before swinging back is (Take g=10 ms−2).

A
0.2 m
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B
0.6 m
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C
8 m
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D
1 m
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Solution

The correct option is A 0.2 mSimple pendulum of length=1mMass=1kgBullet of mass=10−2kgSpeed =2×102m/sHeight to which the bob rises before swimming back(g=10m/s2)Now finding speed of bullet − bob combination after collison =Vusing the law of conservation of momentummv=(m+M)V(0.01)(200)=(0.01+1)VV=1.98m/sh= Height to which the bob of pendulum is raisedusing conservation of energyelectric potential energy gained−Kinetic energy lost(m+M)gh=(0.5)(m+M)V2V=√2gh1.98=√2×10×hh=(1.98)2×2×10=0.2m

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