Work Energy And Power Question 159

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 [CPMT 1989; Kerala PMT 2002]

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:

Initial momentum = $ mv $

Final momentum = $ (m+M)V $

By conservation of momentum $ mv=(m+M)V $

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

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

$ =\frac{1}{2}\frac{m^{2}v^{2}}{M+m} $



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