Question

In a $1\text{D}$ motion, ball $B$ is ahead of $A$. Ball $A$ is moving with a speed of $10\text{m/s}$ towards $B$ and ball $B$ is moving with speed $15\text{m/s}$ towards ball $A$. After the collision, ball $A$ starts moving with a speed of $5\text{m/s}$ towards ball $B$ and ball $B$ starts moving with a speed of $20\text{m/s}$ away from $A$. Find the coefficient of restitution $\left(e\right)$.

• A. $0.3$
• B. $0.4$
• C. $0.8$
• D. $0.6$

Answer 1

The correct option is D $0.6$


Let $u_1$= Speed of ball A before collision = $10\text{m/s}$
$u_2=$ Speed of ball B before collision $=15\text{m/s}$


$v_1=$ Speed of ball A after collision =$5\text{m/s}$
$v_2=$ Speed of ball B after collision =$20\text{m/s}$
The coefficient of restitution $\left(e\right)=\frac{\text{speed of separation}}{\text{speed of approach}}$
Speed of separation $=v_2-v_1$
Speed of approach $=u_1+u_2$

$\therefore e=\frac{v_2-v_1}{u_1+u_2}$
$\Rightarrow e=\frac{20-5}{10+15}=\frac{15}{25}=0.6$