A bag (mass M) hangs by a long thred and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag+bullet) system -

Options

A. Momentum is `(mv M)/(M+m)`
B. Kinetic energy is `(mv^(2))/(2)`
C. Momentum is `(mv(M+m))/(M)`
D. Kinetic energy is `(m^(2)v^(2))/(2(M+m))`

Answer

D

Explanation

Initial momentum = mv
Final momentum = (m + M)V
By conservation of momentum `mv= (m + M)V`
`therefore` Velocit of (bag + bullet) system `V= (mv)/(M + m)`
`therefore` Kinetic energy `= (1)/(2) (m+M)V^(2)`
`=(1)/(2) (m + M) ((mv)/(M+ m))^(2) = (1)/(2) (m^(2) v^(2))/(M + m)`