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There is a circular tube in a vertical plane. Two liquids which do not mix of densities $d_{1} a n d d_{2}$ are filled in tube. Each liquid subtends 90° at the centre. If radius joining their interface makes an angle $α$ with the vertical, then $\frac{d_{1}}{d_{2}} =_______$

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$\frac{1 + \sin α}{1 - \cos α}$

$\frac{1 + \sin α}{1 - \sin α}$

$\frac{1 + \cos α}{1 - \cos α}$

$\frac{1 + \tan α}{1 - \tan α}$

answer is D.

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Detailed Solution

Pressure due to 1 = Pressure due to 2

$d_{2} g (R \sin α + R \cos α) = d_{1} g (R \cos α - R \sin α) ∴ \frac{d_{1}}{d_{2}} = \frac{\sin α + \cos α}{\cos α - \sin α} \Rightarrow \frac{d_{1}}{d_{2}} = \frac{1 + \tan α}{1 - \tan α}$

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