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 makes an angle `alpha` with vertical . rartio `d_(1)//d_(2)` is

Options

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

Answer

A

Explanation

Equating pressure at A
`(Rcosalpha+Rsinalpha)d_(2)g=(Rcosalpha-Rsinalpha)d_(1)g`
`Rightarrow(d_1)/(d_2)=(cosalpha+sinalpha)/(cosalpha-sinalpha)=(1+tanalpha)/(1-tanalpha)`