A particle of mass m moving with speed u collides perfectly inelastically with another particle of mass 2m at rest. Find loss of kinetic energy of system in the collision.

Explanation

Let velocity of system of particles after collision is v.
By law of momentum conservation,
`m u = 3mv rArr v=(u)/(3)`
Now, loss of kinetic energy `=K_(i)-K_(f)`
`rArr" "DeltaK=(1)/(2)m u^(2)-(1)/(2)3m[(u)/(3)]^(2)`
`rArr" "DeltaK=(1)/(2) m u^(2)-(1)/(6)m u^(2)`
`rArr" "DeltaK=(1)/(3)m u^(2)`