A ball A, moving with kinetic energy E, makes a head- on elastic collision with a stationary ball with mass ‘n’ times that of A. The maximum potential energy stored in the system during the Collison is

Let A have mass ‘m’ and initial velocity ‘u’

 ${\mathrm{E}}_{\mathrm{i}}=\frac{1}{2}{\mathrm{mu}}^2=\mathrm{E}$ 

and momentum P = mu = constant. 

The potential energy becomes maximum when the kinetic energy is minimum. This occurs when the bodies move the same velocity maximum kinetic energy.

${\mathrm{E}}_{\mathrm{f}}=\frac{{\mathrm{P}}^2}{2(\mathrm{m}+\mathrm{nm})}$

Maximum potential energy ${\mathrm{E}}_{\mathrm{i}}-{\mathrm{E}}_{\mathrm{f}}=\frac{1}{2}{\mathrm{mu}}^2-\frac{{\mathrm{m}}^2{\mathrm{u}}^2}{2\mathrm{m}(1+\mathrm{n})}=\frac{\mathrm{nE}}{\mathrm{n}+1}$