A bullet of mass `m` moving with velocity `u` on smooth surface strikes a block of mass `M` kept at rest. The collision is completely inelastic. Find the common velocity and the fractional loss in kinetic energy.

Explanation

By the momentum conservation
`mu + M xx 0 = (m + M)v`
`rArr v = ( m u)/(m + M)`
Loss in `K.E., Delta K = (1)/(2) (m M)/( m + M) ( u - 0)^(2)`
Incident `K.E., K_(1) = (1)/(2) m u^(2)`
Fractional loss in `K.E. = (Delta K)/(K_(i)) = (M)/(M + m)`