There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in the tube. Each liquid subtends 90° angle at centre. Radius joining their interface makes an angle α with vertical. Ratio is:

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Question

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 90° angle at centre. Radius joining their interface makes an angle α with vertical. Ratio $\frac{d_{1}}{d_{2}}$ is:

$\frac{1 + sinα}{1 - sinα}$

$\frac{1 + cosα}{1 - cosα}$

$\frac{1 + tanα}{1 - tanα}$

$\frac{1 + sinα}{1 - cosα}$

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d₂ × A sin α + $\frac{d}{2}$ × R cos α

= d₁ (R cos α – R cos α)

$\frac{d_{2}}{d_{1}} = \frac{cosα - sinα}{sinα + cosα}$