# Two small particle of equal masses start moving in opposite direction from A in a horizontal circular path of radius r Their tangential velocity at A are v and 2v, respectively as shown. Where will be the first collision in the path of the circle.

a) at distance $\pi \;r$  anticlockwise from A

b) at distance $\large\frac{2\pi}{3} $$r anticlockwise from A c) at distance \large\frac{\pi}{2}$$r$  clockwise from A

d) at distance $\large\frac{\pi \;r}{2}$  anticlockwise from A

Let the two make the first collision in time t,
distance travelled by particle 1 with velocity 'v' is $vt$
and distance travelled by particle 2 with velocity $2v=2vt$
$vt + 2vt=2 \pi r$
$\therefore t=\large\frac{2 \pi r}{3v}$
Distance travelled by particle with velocity $v =v \times \large\frac{2 \pi r}{3 v}$
$\qquad=\large\frac{2 \pi r}{3}$
So the first collision will take place at distance $\large\frac{2 \pi r}{3}$ in anticlockwise from A
Hence b is the correct answer.

edited Feb 17, 2014 by meena.p