1. Tardigrade
  2. Question
  3. Physics
  4. A cylindrical block floats vertically in a liquid of density ρ1 kept in a container such that the fraction of volume of the cylinder inside the liquid is x1. then some amount of another immiscible liquid of density ρ2 (ρ2 < ρ1) is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with x2 fraction of volume of the cylinder inside the liquid of density ρ1. The ratio ρ1/ρ2 will be

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Q. 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 $\rho_2 (\rho_2 < \rho_1)$ 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

WBJEEWBJEE 2013Mechanical Properties of Fluids

Solution:

The given situation is shown as
image
As the Bouyant force in both the cases are same
$\therefore \rho_{1} x_{1} g=\rho_{1} x_{2} g+\rho_{2}\left(1-x_{2}\right) g$
On solving $\frac{\rho_{1}}{\rho_{2}}=\frac{\left(1-x_{2}\right)}{\left(x_{1}-x_{2}\right)}$