Clearly the two particles are at the two ends of the diameter of a circular path. It is further clear that each particle will return to its initial position after describing one circle.

If t = required time then,

t = \(\frac{2\pi r}{v}=\frac{\pi d}{v}\)

Where,

v = speed of particles.

r = radius of the circular track

d = constant distance between particles

2r = diameter of the circular path