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

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

• B

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

• C

  $\frac{\mathrm{\pi r}}{\mathrm{V}}$

• D

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