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:

• A. momentum is $\frac{mvM}{M+m}$
• B. kinetic energy is $\frac{m{v}^2}{2}$
• C. Mmomentum is $\frac{mv(M+m)}{M}$
• D. Kinetic energy is $\frac{m^2{v}^2}{2(M+m)}$

Answer 1

The correct option is D Kinetic energy is $\frac{m^2{v}^2}{2(M+m)}$

From conservation of momentum
$mv+M\left(0\right)=(m+M)v^{\prime }$
$v^{\prime }=\frac{mv}{M+m}$
K.E. acquired by (Bag $+Bullet$) system $=\frac{1}{2}m{v}^{\prime 2}$
$=\frac{1}{2}m{\left(\frac{mv}{M+m}\right)}^2=\frac{m^2{v}^2}{2(M+m)}$