A particle of mass m1 collides head-on with another stationary particle of mass m2 m2>m1. The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

For conservation of momentum, we have,m1v1=m1+m2v or v=m1/m1+m2v1​ Now the loss of energy =Ki−Kf=12m1v12−12m1+m2v2​∴ Fraction of energy lost=Ki−KfKi ​=12m1v12−12m1+m2v212m1v1                                                             =1−m1+m2/m1×v2/v12​=1−m1+m2/m1×m1v12/m1+m22×1/v12​=1−m1m1+m2=m2/m1+m2