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 radius of horizontal circular path of eachmass is same
C. all masses revolve in the same horizontal plane
D. all the particles must have same mass.

Answer

C

Explanation

For conical pendulum l , mass m moving
along horizontal circle is 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))`
` lcos theta` is the vertical distance of below O point of suspension. hence if `omega` of all three pendulum are same, they small 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 path of bob below point of suspension. If T is same for three pendulum
even L shall be also same. hence all three particles shall revolve in same horizontal plane