Question

A metal ball falls from a height of 1 m on to a steel plate and jumps upto a height of 81 cm. Find the coefficient of restitution of the ball material.

• A. 0.2
• B. 9
• C. 0.9
• D. 90

Answer 1

Answer: (C)

0.9

Let
$u_1=$Velocity of ball before collision
$v_1=$Velocity of ball after collision
$u_2=$Velocity of plate before collision$=0$
$v_2=$Velocity of plate after collision$=0$
The coefficient of restitution$\left(e\right)$ is given by,
$e=-\frac{Relativevelocityofballaftercollision}{Relativevelocityofballbeforecoliision}$
$e=-\frac{v_1-v_2}{u_1-u_2}$
$\Rightarrow e=-\frac{-v_1-0}{u_1-0}=\frac{v_1}{u_1}$
Using $v_1^2=2g{h}_1\Rightarrow v_1=\sqrt{2g{h}_1}$
Using $u_1^2=2g{h}_2\Rightarrow u_1=\sqrt{2g{h}_2}$
$\Rightarrow e=\frac{\sqrt{2g{h}_1}}{\sqrt{2g{h}_2}}=\sqrt{\frac{h_1}{h_2}}$
Here, $h_1=100$cm$,h_2=90$cm
$e=\sqrt{\frac{h_2}{h_1}}=\sqrt{\frac{81}{100}}=0.9$