Question

A bag P (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 (beg + bullet) system the

• A. Momentum is $\frac{mvM}{M + m}$
• B. Kinetic energy $\frac{mV^{2}}{2}$
• C. Momentum is $\frac{mv(M + m)}{M}$
• D. Kinetic energy is $\frac{m^{2}V^{2}}{2(M + m)}$

Answer 1

Answer: (D)

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

Answer 2

Velocity of combined system $V = \frac{mv}{m + M}$

Momentum for combined system

$= (m + M)V = (m + M)\frac{mv}{m + M}$

Kinetic energy for combined system

$$$= \frac{m^{2}v^{2}}{2(m + M)}$.