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 2v 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?

First collision will occur at an angle of 120° from the starting point since one particle will cover an angle twice that of the other one, and the sum of the two angles will be 360°. Next, due to elastic collision, velocities will exchange. Similarly, the next collision will occur at an angle of 120° from this position. Then the next collision will occur at A. Hence there will be 2 collisions before meeting again at A.