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

From the figure, we have
`delta gR(cos theta+sin theta)=rho gR(cos theta - sin theta)`
`implies delta cos theta+ delta sin theta= rho cos theta- rho sin theta`
`implies sin theta(delta+rho)=cos theta(rho-delta) implies tan theta=(rho-delta)/(rho+delta)`