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A double conical pendulum consists of two masses, m and M connected by a massless string passing over a frictionless, massless pulley. The entire apparatus rotates freely at constant angular speed $ω$ (rad/s) about the vertical axis (dashed line) passing through center of pulley as shown. After the system comes in steady state, the length of string on either sides of pulley are $l$ and L as shown. Pick up the correct option(s).

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$\cos ϕ = \frac{g}{ω^{2} l}$

$\cos θ = \frac{g}{ω^{2} L}$

$m l = M L$

$\frac{\cos ϕ}{\cos θ} = \frac{m}{M}$

answer is A, B, C, D.

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Detailed Solution

$T \cos θ = M g$

$T \cos ϕ = m g$

$T \sin ϕ = m l \sin ϕ ω^{2}$

$T \sin θ = M l \sin θ ω^{2}$

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