Physics - Fluid Question with Solution | TestHub

$V=$ Volume of solid sphere. Let $V_1=$ Volume of the part of the sphere immersed in a liquid of density ${\rho }_1$ and $V_2=$ Volume of the part of the sphere immersed in liquid of density ${\rho }_2$. According to law of floatation,
Hence from eqns (i) and (ii), $\begin{array}{rl}& V_1\rho g+V_2\rho g=V_1{\rho }_{1}g+V_2{\rho }_{2}g\\ & \text{ or }{V}_1\left(\rho -{\rho }_1\right)g=V_2\left({\rho }_2-\rho \right)g\\ & \text{ or }\frac{V_1}{V_2}=\frac{{\rho }_2-\rho }{\rho -{\rho }_1}\end{array}$