A uniform long tube is bent into a circle of radius R and it lies in vertical plane. Two liquids of same volume but densities `rho " and " delta` fill half the tube. The angle `theta` is

Options

A. `tan^(-1)((rho-delta)/(rho+delta))`
B. `tan^(-1)""(rho)/(delta)`
C. `tan^(-1)""(delta)/(rho)`
D. `tan^(-1)((rho+delta)/(rho-delta))`

Answer

A

Explanation

`h_1=R sin theta+R cos theta`
`h_2=R-R cos theta`
`h_3=R-R sin theta`
`delta g h_1+rho g h_2=rho g h_3`
`implies delta g R(sin theta+cos theta)+rho g R(1-cos theta)=rho g R(1-sin theta)`
`implies tan theta=(rho-delta)/(rho+delta) implies theta=tan^(-1)((rho-delta)/(rho+delta))`.