There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^o$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{{{d_1}}}{{{d_2}}}$ is
JEE MAIN 2014, Diffcult
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Equating pressure at $A$
$\left( {R\cos \alpha + R\sin \alpha } \right){d_2}g = \left( {R\cos \alpha - R\sin \alpha } \right){d_1}g$
$ \Rightarrow \frac{{{d_1}}}{{{d_2}}} = \frac{{\cos \alpha + \sin \alpha }}{{\cos \alpha - \sin \alpha }} = \frac{{1 + \tan \alpha }}{{1 - \tan \alpha }}$
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