Question

Body $A$ of mass $m$ and $B$ 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.
  $\frac{2\pi r}{3V}$
  
• B.
  $\frac{\pi r}{V}$
  
• C.
  $\frac{2\pi r}{V}$
  
• D.
  $\frac{\pi r}{2V}$
  

Answer 1

The correct option is A

$\frac{2\pi r}{3V}$

As given, the collision is elastic,
Coefficient of restitution,
$e=\frac{\text{velocity of seperation after collision}}{\text{velocity of approch before collision}}=1$
$e=1=\frac{\text{Velocity of separation}}{2V-(-V)}$
Velocity of separation $=3V$
So, time required for the one revolution $=\frac{2\pi r}{3V}$
Final answer: (d)