Two particles move on a circular path (one just inside and the other just outside) with the angular velocities `omega` and `5omega` starting from the same point. Then

Options

A. they cross each other at regular intervals of time
`(24pi)/(4 omega)` when their angular velocities are oppositely directed
B. they cross each other at points on the path subtending an angle of `60^(@)` at the centre if their angular velocities are oppositely directed
C. they cross at intervals of time `(pi)/(3 omega)` if their angular velocities are oppositely directed
D. they cross each other at points on the path subtending `90^(@)` at the centre if their angular velocities are in the same sense

Explanation

If the angular velocities are oppositely directed, they meet at intervals of
time t = `(2pi)/(omega_(rel)) = (2pi)/(6 omega) = (pi)/(3omega)`
Angle subtended at the centre by the crossing pint
`theta = omega t = (pi)/(3) = 60^(@)`
When their angluar velocities are in the same direction,
t' = `(2pi)/(omega_(rel)) = (2pi)/(4 omega) = (pi)/(2 omega) and theta' = (pi)/(2 omega) xx omega = (pi)/(2)`