Question

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

• A. $eh$
• B. $e^{2}h$
• C. $e^{3}h$
• D. $e^{4}h$

Answer 1

The correct option is D $e^{4}h$

The velocity attained after a fall through a height h is given by $v^2=2gh$
Thus $h\propto v^2$ The velocity after first rebound is ev. Therefore, the height attained after first rebound = $e^{2}h$. Velocity after second rebound is $e^{2}v$. Hence the height attained after second rebounds is $e^{4}h$. Thus the correct choice is (d).