Question

A small ball on a frictionless horizontal surface moves towards right with a velocity $V$. It collides with the wall and returns back and continues to and fro motion. If the average speed for first to and fro motion of the ball is $\left(\frac{2}{3}\right)V$, then the coefficient of restitution of impact is:

• A. $0.5$
• B. $0.8$
• C. $0.25$
• D. $0.75$

Answer 1

The correct option is A $0.5$

Time during to motion is $t_1=\frac{s}{V}$

Time during fro motion is $t_2=\frac{s}{eV}$

Total time is $t=t_1+t_2$

Total distance is $2s$

So, average speed is $\frac{2s}{t}=\frac{2s}{(\frac{s}{V}+\frac{s}{eV})}=\frac{2eV}{(1+e)}=\frac{2V}{3}\Rightarrow e=0.5$