A cylindrical block floats vertically in a liquid of density ρ 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 immisci

Question

A cylindrical block floats vertically in a liquid of density $ρ_{1}$ 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 $ρ_{2} (ρ_{2} < ρ_{1})$ 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 $ρ_{1}$ . The ratio $ρ_{1} / ρ_{2}$ will be

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Answer:

A

Solution:

The given situation is shown asAs the Bouyant force in both the cases are same $∴$ $ρ_{1} x_{1} g = ρ_{1} x_{2} g + ρ_{2} (1 - x_{2}) g$ On solving $\frac{ρ _{1}}{ρ _{2}} = \frac{( 1 - x _{2} )}{( x _{1} - x _{2} )}$

TestHub · Accepted Answer

The given situation is shown as As the Bouyant force in both the cases are same ∴ ρ 1 ​ x 1 ​ g = ρ 1 ​ x 2 ​ g + ρ 2 ​ ( 1 − x 2 ​ ) g On solving ρ 2 ​ ρ 1 ​ ​ = ( x 1 ​ − x 2 ​ ) ( 1 − x 2 ​ ) ​

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