A bag of mass `M` hangs by a long massless rope. A bullet of mass in, moving horizontally with velocity `u`, is caught in the bag. Then for the combined (bag `+` bullet) system, just after collision

Options

A. Momentum is `mMv//(M + m)`
B. kinetic energy is `(1//2)Mv^(2)`
C. Momentum is `mv`
D. kinetic energy is `m^(2)v^(2)//2(M + m)`

Answer

C, D

Explanation

`COLM : m u + 0 = (m + M)v rArr v = ((m)/(M + m))u`
`KE` after collision
`= (1)/(2) (m + M) xx ((m)/(m + M))^(2) u^(2) = (m^(3)u^(2))/(2(m + M))`