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. $Momentumis\frac{mvM}{M+m}$
• B. $Kineticenergyis\frac{m{v}^2}{2}$
• C. $Momentumis\frac{mv(M+m)}{M}$
• D. $Kineticenergyis\frac{m^2{v}^2}{2(M+m)}$

Answer 1

The correct option is D

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

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

$=\frac{1}{2}(m+M){\left(\frac{mv}{M+m}\right)}^2=\frac{1}{2}\frac{m^2{v}^2}{M+m}$