Question

A body falling from a height of $10m$ rebounds from hard floor. If it loses $20\%$ energy in the impact, then coefficient of restitution is

• A. $0.89$
• B. $0.56$
• C. $0.23$
• D. $0.18$

Answer 1

The correct option is A $0.89$

As 20% energy lost in collision therefore

$mg{h}_2=80$ % of $mg{h}_1\Rightarrow \frac{h_2}{h_1}=0.8$

Here$h\propto v^2$

and $e=\frac{v_f}{v_i}$

so in such cases:

$e=\sqrt{\frac{h_2}{h_1}}=\sqrt{0.8}=0.89$