A thin uniform circular tube is kept in a vertical plane. Equal volume of two immiscible liquids whose densites are `rho_(1)` and `rho_(2)` fill half of the tube as shown. In equilibrium the radius passing through the interface makes an angle of `30^(@)` with vertical. The ratio of densities `(rho_(1)//rho_(2))` is equal to

Options

A. `(sqrt(3)-1)/(2-sqrt(3))`
B. `(sqrt(3)+1)/(2+sqrt(3))`
C. `(sqrt(3)-1)/(sqrt(3)+1)`
D. `(sqrt(3)+1)/(sqrt(3)-1)`

Answer

D

Explanation

`tan theta = (rho_(1)-rho_(2))/(rho_(1)+rho_(2)) = tan 30^(@) = (1)/(sqrt(3))`
Solving this equation we get,
`(rho_(1))/(rho_(2)) = (sqrt(3)+1)/(sqrt(3)-1)`