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 $A$ [2009]

Question

Smart Achievers · Accepted Answer

(3)

According to question, between collision, the particles move with constant speed.

At first collision one particle having speed $2 v$ will rotate $2 \times 120 ° = 240 °$ while other particle having speed $v$ will rotate $120 °$ . Hence, first collision takes place at B. At first collision, they will exchange their velocities as the collision is elastic and the particles have equal masses. Again second collision takes place at C.

Now, as shown in figure, after two collisions they will again reach at point A.

Solution

1 4

2 3

3 2

4 1

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