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 ​d₁/d₂​​ is ______.

विकल्प

• `(1+sinalpha)/(1-sinalpha)`

• `(1+cosalpha)/(1-cosalpha)`

• `(1+tanalpha)/(1-tanalpha)`

• `(1+sinalpha)/(1-cosalpha)`

Answer 1

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 ​d₁/d₂​​ is `underlinebb((1+tanalpha)/(1-tanalpha))`.

Explanation:

(R cosα + R sinα)d₂g = (R cosα - R sinα)d₁g

⇒ `"d"_1/"d"_2=(cosalpha+sinalpha)/(cosalpha-sinalpha)=(1+tanalpha)/(1-tanalpha)`