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 ?

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 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 (C) 2 (D) 1

Tardigrade Admin · Accepted Answer

At first collision one particle having speed

2 v

will rotate

24 0^{\circ}

(

or

\frac{4 π}{3})

while other particle having speed

v

will rotate

12 0^{\circ}

(or

\frac{2 π}{3})

.
At first collision they will exchange their velocities. Now as shown in figure, after two collisions they will again reach at point

A

.

4

3

2

1

At first collision one particle having speed 2v will rotate 240∘ ( or 34π​) while other particle having speed v will rotate 120∘ (or 32π​). At first collision they will exchange their velocities. Now as shown in figure, after two collisions they will again reach at point A.