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)} $
Show Answer
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} $
