Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$ respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$, these two particles will again reach the point $A$ ?

• A

  4
• B

  3
• Correct answer
  C

  2
• D

  1

Solution

At first collision one particle having speed $2 v$ will rotate $240^{\circ}\left(\right.$ or $\left.\frac{4 \pi}{3}\right)$ while other particle having speed $v$ will rotate $120^{\circ}$ (or $\left.\frac{2 \pi}{3}\right)$. At first collision they will exchange their velocities. Now as shown in figure, after two collisions they will again reach at point $A$.

Hence, the correct answer is option: 'C'.