A bullet of mass 'm' moving with velocity 'u' passes through a wooden block of mass `M = nm` as shown in figure. The block is resting on a smooth horizontal floor. After passing through the block, velocity relative to the block is
.

Explanation

Let `v'` ve the velocity of block. Then from conservation of linear momentum.
`m u = mv + mnv'` (or) `v = ((u-v)/(n))`
`:.` velocity of bullet relative to block will be
`v_(r)=v-v'=v-((u-v)/(n))=((1+n)v-u)/(n)`.