IIT-JEE 2009 · Paper 1 · Physics Q45

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PhysicsSingle correct+3 / -1Question 45 of 60

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 horizontal circle with the point A at the top; two particles start at A, one moving to the left with speed v and the other to the right with speed 2v.

Answer and worked solution

Official answer: C

Exchange of velocities. In an elastic collision of equal masses the velocities are exchanged, so the motion looks like two "velocity carriers" ( $v$ and $2v$ ) passing through each other; the particles simply take turns carrying them.

Meetings. The carriers meet every time their total distance is one circumference, i.e. every $\frac{2\pi R}{3v}$ . Both are back at A when the slow carrier has gone round once (time $\frac{2\pi R}v$ ), the fast one twice. In that time they meet 3 times, the third meeting being at A itself.

So there are 2 collisions before the particles are together at A again.

(C) 2

Topics:Elastic and inelastic collisions Uniform circular motion

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IIT-JEE 2009 · Paper 1, Physics question 45