In a free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M distance D away from it. When the bullet has moved through a distance d towards the bnlock, the center of mass of the bullet-block system is at a distance of

Options

A. `((D-d)m)/(M+m)` from the block
B. `(md+MD)/(M+m)` from the rifle
C. `(2dm+DM)/(M+m)` from the rifle
D. `(D-d)=(M)/(M+m)` from the bullet

Answer

A, D

Explanation

centre of mass is located at distance `r_(2)` from block
`Mr_(2)=mr_(1) , Mr_(2)=m(D-d-r_(2))`
`r_(2)=(m(D-d))/(M+m)`
also `M(D-d-r_(1))=mr_(1)`
so `r_(1)=(M(D-d))/(M+m)` distance of `COM` from bullet