A steel ball falls from a height h on a floor for which the coefficient of restitution is e. The height attained by the ball after two rebounds is

The velocity attained after a fall through a height h is given by

${\mathrm{v}}^2=2\mathrm{gh}$

Thus $\mathrm{h}\propto {\mathrm{v}}^2$. The velocity after first rebound is ev. Therefore, the height attained after first rebound $={\mathrm{e}}^2\mathrm{h}$. Velocity after second rebound is ${\mathrm{e}}^2\mathrm{v}$. Hence the height attained after rebound is second ${\mathrm{e}}^4\mathrm{h}$. Thus the correct choice is (4).