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 substends `90^@` angle at centre. Radius joining their interface make an angle `alpha` with vertical. Ratio `(d_1)/(d_2)` is :

Options

A. `(1+sin aplha)/(1-sin alpha)`
B. `(1+cos aplha)/(1-cos alpha)`
C. `(1+tan aplha)/(1-tan alpha)`
D. `(1+sin aplha)/(1-cos alpha)`

Answer

C

Explanation

(c) Pressure at interface A must be same from both the
sides to be in equilibrium.

`:. (Rcos alpha+Rsin alpha)d_2g= (Rcos alpha-Rsin alpha)d_1g`
`implies(d_1)/(d_2)= (cos alpha+sin alpha)/(cos alpha-sin alpha)=(1+tan alpha)/(1-tan alpha)`