A solid of uniform density floats at the common interface of two immiscible

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

A solid of uniform density

\rho_{\text{s}}

floats at the common interface of two immiscible, non-mixing liquids of densities

\rho_{1}

(upper) and

\rho_{2}

(lower), where

\rho_{1} < \rho_{\text{s}} < \rho_{2}

. If the total volume of the solid is

V

and the volume immersed in the lower liquid is

V_{2}

, derive an expression for the ratio

\dfrac{V_{2}}{V}

in terms of

\rho_{1}

\rho_{2}

and

\rho_{\text{s}}