Question

A bag P (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity $v$ the bag , then for the combined (bag+bullet) system

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

Answer 1

Answer: (D)

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

Using conservation of momentum,

$mv=Mu+mu$

$u=\frac{mv}{M+m}$

Kinetic energy for combined(bag + bullet) system $=\frac{1}{2}\times (M+m)\times (\frac{mv}{M+m}{)}^2$

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