Question

A body is allowed to fall on the ground from a height $h_1$. If it is rebound to a height $h_2$ then the coefficient of restitution is:

• A. $\frac{h_2}{h_1}$
• B. $\sqrt{\frac{h_2}{h_1}}$
• C. $\frac{h_1}{h_2}$
• D. $\sqrt{\frac{h_1}{h_2}}$

Answer 1

The correct option is B $\sqrt{\frac{h_2}{h_1}}$

When a ball is dropped from a height h₁, the velocity before reaching ground is
$v=\sqrt{2g{h}_1}$
When the ball rebounces to a height h₂, the velocity just after impact was

$v^{\prime }=\sqrt{2g{h}_2}$

Coefficient of restitution

$=\frac{\sqrt{2g{h}_2}}{\sqrt{2g{h}_1}}=\sqrt{\frac{h_2}{h_1}}$

Hence,

option $B$ is correct answer.