Two particles are moving with constant speed `v` such that they are always at a constant distance `d` apart and their velocities are always equal and opposite. After what time will they return to their initial positions ?

Explanation

Since, the particles while moving with constant speed (v) are always at a constant distance (d), they must be at the two ends of the diameter of a circular path. The diameter of this circular path `=d`. Each particle will return to its initial position after describing a circular path `= 2 pi r = pi d`
( :. 2 r =d) Time interval after which each particle will return to its intial position
=distance travelled//speed =pi d//v`.