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A bullet of mass $m$ and speed $v$ hits a pendulum bob of mass $M$ at time $t = t_{1}$ and passes completely through the bob. The bullet emerges at time $t = t_{2}$ with a speed of $v / 2$ . The pendulum bob is suspended by a light, rigid rod of length $l .$ After the collision, the bob can barely swing through a complete vertical circle. At time $t = t_{3}$ the bob reaches the highest position What quantities are conserved in this process?

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total momentum of the bob and the bullet during the time interval $∆ t = t_{2} - t_{1}$

Momentum of the bob after $t = t_{2}$

total mechanical energy of the bob and the bullet during the time interval $∆ t = t_{3} - t_{1}$

total kinetic energy of the bob and the bullet during the time interval $∆ t = t_{2} - t_{1}$

answer is B.

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Detailed Solution

Since along the line of impact, there is no net external force acting on the ball & bob system so the
conservation of linear momentum is valid during $∆ t = t_{2} - t_{1}$

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