Rotational Motion Question 102

Question: A bag (mass $M$ ) hangs by a long thread and a bullet (mass $m$ ) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined (bag + bullet) system

Options:

A) Momentum is $\frac{mvM}{M+m}$

B)Kinetic energy is $\frac{mv^{2}}{2}$

C)Momentum is $\frac{mv{{(M+m)}^{{}}}}{M}$

D)Kinetic energy is $\frac{m^{2}v^{2}}{2(M+m)}$

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Answer:

Correct Answer: D

Solution:

[d] Initial momentum =mv Final momentum = (m+M)V By conservation of momentum $

$mv=(m+M)V$

$\therefore $ Velocity of (bag +bullet) system $V=\frac{mv}{M+m}$

$\therefore $ Kinetic energy $=\frac{1}{2}(m+M)V^{2}$ $=\frac{1}{2}(m+M){{\left( \frac{mv}{M+m} \right)}^{2}}=\frac{1}{2}\frac{m^{2}v^{2}}{(M+m)}$



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