A ball of mass m makes head-on elastic collision with a ball of mass nm which is initially at rest. . Find the the value of n for which the transfer the transfer of energy by the first ball is maximum.

Let u be the initial velocity of the ball of mass m. Thenmu=mv1+nmv2⇒v1+nv2=u                 …(i)For elastic collision, Newton's experimental formula is u2=0v1−v2=−u1−u2⇒v1−v2=−u         …(ii)Solving Eqs. (i) and (ii), v1=1−n1+nuFractional loss in KE (= fractional transfer of KE)f=Ki−KfKi−12mu2−12mv1212mu2=1−v1u2f=1−1−n1+n2=4n(n+1)2The transfer of energy is maximum when f=1 or 100%4n(n+1)2=1⇒n=1That is, the transfer of energy is maximum when the mass ratio is unity.