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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