Question

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?

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

First collision will occur at an angle of ${120}^0$ from starting point since one particle will cover angle twice of the other one and sum of the two angles will be ${360}^0$. Next, due to elastic collision, velocities will exchange. Similarly, next collision will occur at an angle ${120}^0$ from this position. Then the next collision will occur at A. Hence there will be 2 collisions before meeting again at A.