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

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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

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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.

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