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. the cross each other at regular intervals of time `2pi//4omega` when their angular velocities are oppositely directed
B. they cross each other at point on the path subtending an angle of `60^@` at the centre if their angular velocities are oppositely directed
C. the cross at intervals of time `pi//3omega` if their angular velocities are oppositely directed
D. they cross each other at points on the path subtendingf `90^` at the centre if their angular velocities are in the same sence

Answer

B, C, D

Explanation

If the velocities are oppositely directed,

Let they cross A at time t, then
`theta=omegat, 2pi-theta=5omegatimplies2pi=6omegatimpliest=pi//3omega`
`theta=omegat, (omegapi)/(3omega)=pi/3=60^@`
If angular velocities are in same sense:
`theta=omegat, 2pi+theta=5s, impliestheta=pi//2`