Question

A ball is dropped from a height 8 m on a smooth horizontal surface. If height attained by the ball after the second collision is 2 m, then the coefficient of restitution is :

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (D)

$\frac{1}{\sqrt{2}}$

Given,

$h^{\prime }=2m$

$h=8m$

$n=2$

The coefficient of restitution and height relationship is given by,

$h^{\prime }=e^{2n}h$

$2=e^4\times 8$

$e^4=\frac{1}{4}$

$e=\frac{1}{\sqrt{2}}$

The correct option is D.