Question

Body $A$ of mass $m$ and body $B$ of mass $3m$ move towards each other with velocities $V$ and $2V$ respectively from the positions as shown, along a smooth horizontal circular track of radius $r$. After the first elastic collision, they will collide again after the time

• A. $\frac{2\pi r}{V}$
• B. $\frac{\pi r}{2V}$
• C. $\frac{\pi r}{V}$
• D. $\frac{2\pi r}{3V}$

Answer 1

The correct option is D $\frac{2\pi r}{3V}$

As collision is elastic,
$e=1=\frac{\text{Velocity of separation}}{2V-(-V)}$
Velocity of separation $=3V$
Velocity of separation $=\frac{\text{displacement}}{\text{time}}$
Required time $=\frac{2\pi r}{3V}$