A large mass 'M' moving with a velocity 'v' collides head-on with a very small mass 'm' at rest - Physics - Work Energy and Power

Question

A large mass 'M' moving with a velocity 'v' collides head-on with a
very small mass 'm' at rest If the collision is elastic, obtain an
expression for the energy lost by the large mass M (take M+m=M)

Ved Prakash Lakhera · Accepted Answer

According to law of conservation of momentum,       MV=M+mV1          V1=MVM+mAccording to law of conservation of energy,            12MV2=12M+mV12Energy of larger mass=12MV12=12MMVM+m2=12M3V2M+m2Now the loss of energy of larger mass ∆E=12MV2-12M3V2M+m2=12MV2M2+m2+2Mm-M2M+m2       Therefore          ∆E=12MV2mm+2MM+m2=12mm+2MMV2

A large mass 'M' moving with a velocity 'v' collides head-on with a very small mass 'm' at rest. If the collision is elastic, obtain an expression for the energy lost by the large mass M (take M+m=M)