College Physics (7th Edition)

(a) There is complete transfer of energy for $m_1=m_2$.
Kinetic energy is given by $K=\frac{p^2}{2m}$. Initial kinetic energy for this elastic collision, $K_i=\frac{p^2}{2m_1}$ For a $m_1$ hitting a stationary $m_2$ and complete transfer of energy, Final kinetic energy is $K_f=\frac{p^2}{2m_2}$, since momentum is conserved. From the second condition for elastic collision - \begin{align*} K_i&=K_f\\ or,\, \frac{p^2}{2m_1}&=\frac{p^2}{2m_2}\\ or,\, m_1 &=m_2 \end{align*}