A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

Explanation

Hint : `k_(1)="Total KE before collision"=(1)/(2)mv^(2)+(1)/(2)(3m)v`
`k_(1)="Total KE after collision"=(1)/(2)(4m)V^(2)`
Put the value of V. found in Q. 46
`Deltak="loss of KE"=k_(1)-k_(2)`
`K_(1)="Total KE before collision"=(1)/(2)mv^(2)+(1)/(2)(3m)v^(2)=2mv^(2)`
`K_(2)="Total KE after collision"=(1)/(2)(4m)V^(2)=2m(5)/(8)v^(2)" as "V=sqrt((5)/(8))v`
`=(5)/(4)mv^(2)`
`DeltaK="Loss of Ke during the collision"`
`=K_(1)-K_(2)`
`=2mv^(2)-(5)/(4)mv^(2)`
`DeltaK=(3)/(4)mv^(2)`