Question

A homogenous solid cube of side length L is immersed such that it floats at the liquid-liquid interface with length $\frac{L}{4}$ in the denser liquid as shown in figure. The density of the solid is given by

• A. $\frac{{\rho }_1+3{\rho }_2}{4}$
• B. $\frac{3{\rho }_1+{\rho }_2}{4}$
• C. ${\rho }_1+4{\rho }_2$
• D. $\frac{{\rho }_1+2{\rho }_2}{2}$

Answer 1

The correct option is A $\frac{{\rho }_1+3{\rho }_2}{4}$


$L^3\rho g=\frac{L^3}{4}{\rho }_{1}g+\frac{3L^3}{4}{\rho }_{2}g$
$\rho =\frac{{\rho }_1}{4}+\frac{3{\rho }_2}{4}=\frac{{\rho }_1+3{\rho }_2}{4}$