A cylindrical block floats vertically in a liquid of density `rho_(1)` kept in a container such that the fraction of volume of the cylinder inside the liquid is `x_(1)`. Then some amount of another immiscible liquid of density `rho_(2) (rho_(2) lt rho_(1))` is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with `x_(2)` fraction of volume of the cylinder inside the liquid of density `rho_(1)`. The ratio `rho_(1)//rho_(2)` will be

Options

A. `(1-x_2)/(x_1-x_2)`
B. `(1-x_1)/(x_1+x_2)`
C. `(x_1-x_2)/(x_1+x_2)`
D. `(x_2)/(x_1)-1`

Answer

A

Explanation

`rho_1 x_1 g=rho_1 x_2 g+rho_2(1-x_2)g`
`implies (rho_1)/(rho_2)=(1-x_2)/(x_1-x_2)`.