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 $e^{4}h$

$Ist$ collision

Velocity of strike $=\sqrt{2gh}$

$\Rightarrow$ Velocity of rebound $=e\times \sqrt{2gh}=u$

$\Rightarrow$ height attained $=\frac{u^2}{2g}=\frac{2^2\times 2gh}{2g}$

$=e^{2}h$

$IInd$ collision

Velocity of strike $=\sqrt{29\times e^{2}h}$

$=e\sqrt{2gh}$

Velocity of rebound $=e\times \left(e\sqrt{2gh}\right)$

$=e^2\sqrt{2gh}=v$

$\Rightarrow$ height attained $=\frac{v^2}{2g}=\frac{e^4\times 2gh}{2g}$$8e^{4}h$.