Three masses of small size 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 $\mathrm{\omega }$ (one such circle is drawn in the shown figure.) Then pick up the correct statement.

For conical pendulum of length $\mathrm{\lambda }$ mass m moving along horizontal circle as shown

$\mathrm{T} \cos \mathrm{\theta } = \mathrm{mg}$-------------(i)

$\mathrm{T} \sin \mathrm{\theta } = {\mathrm{m\omega }}^2\mathrm{l} \sin \mathrm{\theta }$--------(ii)

From equation (i) and equation (ii),

$\mathrm{l} \cos \mathrm{\theta } = \frac{\mathrm{g}}{{\mathrm{\omega }}^2}$

$l$ cos $\mathrm{\theta }$ is the vertical distance of bob below O point of suspension. Hence if $\mathrm{\omega }$ of all three pendulums are same, they shall revolve in same horizontal plane.