Question

A metallic sphere floats in an immiscible mixture of water $({\rho }_w={10}^{3}kg/m^3)$and a liquid$({\rho }_l=13.5\times {10}^{3}kg/m^3)$ such that its $\frac{4}{5}$th volume is in water and $\frac{1}{5}$th of the volume in the liquid, Find the density of metal.

Answer 1

Total upthrust = weight of metal sphere
$\therefore \left(\frac{4}{5}V\right)\left({10}^3\right)g+\left(\frac{1}{5}V\right)(13.5\times {10}^5)g$
$=\left(V\right)\left({\rho }_{metal}\right)\left(g\right)$
$\therefore {\rho }_{metal}=3.5\times {10}^{3}Kg/m^3$