Three point masses are attached by light inextensible strings of various lengths to a point O on the ceiling. All of the masses swing round in horizontal circles of various radii with the same angular frequency `omega` (one such circle is drawn in the shown figure.) Then pick up the correct statement.

Options

A. The vertical depth of each mass below point of suspension from ceilling is different.
B. The raduis of horizontal circular path of each mass is same.
C. All masses revolve in the same horizontal plane.
D. All the particles must have same mass.

Explanation

For conical pendulum of length l , mass m moving along horizontal circle as shown
`T cos theta= mg .....(1)`
` T sin theta=m omega^(2)l sin theta.......(2)`
From equation (1) and equation (2) , `l cos theta=g/(omega^(2))`

`l cos theta` is the vertical distance of bob below O point of suspension. hence if `omega` of all three pendulums are same, they shall revolve in same horizontal plane.
Alternate:
If we remember that time period T of conical pendulum is
`T=2pisqrt(L/g)` where L is the vertical depth of bob below point of suspension. if T is same for three pendulums even L shall be also same. hence all three particles shall revolve in same horizontal plane.