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 `"mu"M//(M+m)`
B. kinetic energy is `"mu"^2//2`
C. momentum is `"mu"(M+m)//M`
D. kinetic energy is `m^(2)u^(2)//2(M+m)`

Answer

D

Explanation

Let combined velocilty of the system be `v`
`(m+MV)v="mu"impliesv=("mu")/(m+M)`
`KE=1/2(m+M)v^(2)=(m^(2)u^(2))/(2(M+m))`