Q. 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
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 $\frac{m^{2}v^{2}}{2(M + m)}$
Explanation
(d) [image:6_image96.png]
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 $= \frac{1}{2}\ (m + M)V^{2}$
$= \frac{1}{2}(m + M)\left( \frac{mv}{M + m} \right)^{2} = \frac{1}{2}\frac{m^{2}v^{2}}{M + m}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.