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

Options

A. `(1+sinalpha)/(1-sinalpha)`
B. `(1+cosalpha)/(1-cosalpha)`
C. `(1+tanalpha)/(1-tanalpha)`
D. `(1+sinalpha)/(1-cosalpha)`

Answer

C

Explanation

Equating pressure at `A`, we get
`Rsinalphad_(2)+Rcosalphad_(2)+R(1-costheta)d_(1)=R(1-sinalpha)d_(1)`
`(sinalpha+cosalpha)d_(2)=d_(1)(cosalpha-sinalpha)`
`implies(d_(1))/(d_(2))=(1+tanalpha)/(1-tanalpha)`