Two particles of masses 0.5 kg and 0.25kg moving with velocity 4.0 m`//`s and -3.0m`//` collide head on in a perfectly inelastic collision. Find the velocity of the composite particle after collision and KE lost in the collision.

Explanation

Here, `m_(1)=0.5kg, m_(2)=0.25kg`
`u_(1)=4.0m//s, u_(2)=-3.0m//s`
If v is velosity of composite particle, then from the principla of conservation of linear momentum,
`(m_(1)+m_(2))v=m_(1)u_(1)+m_(2)u_(2)`
`(0.5+0.25)v=0.5xx4+0.25(-3.0)`
`v=(2xx0.75)/(0.75)=(1.25)/(0.75)=1.67m//s`
KE lost `=(1)/(2)m_(1)u_(1)^(2)+(1)/(2)m_(2)u_(2)^(2)-(1)/(2)(m_(1)+m_(2))v^(2)`
`=(1)/(2)xx0.5xx4^(2)+(1)/(2)xx0.25xx(-3.0)^(2)`
`-(1)/(2)(0.5+0.25)((5)/(3))^(2)`
`=4+(9)/(8)-(25)/(24)=(98)/(28)=4.1J`