Question

A metallic sphere floats in an immiscible mixture of water $({\rho }_w={10}^{3}kg/m^3)$ and a liquid $({\rho }_L=13.5\times {10}^{3}kg/m^3)$ with (1/5)th portion by volume in the liquid and remaining in water. The density of the metal is:

• A. $4.5\times {10}^{3}kg/m^3$
• B. $4.0\times {10}^{3}kg/m^3$
• C. $3.5\times {10}^{3}kg/m^3$
• D. $1.9\times {10}^{3}kg/m^3$

Answer 1

The correct option is C $3.5\times {10}^{3}kg/m^3$

Since weight of body = buoyant force

${\varrho }_m\times V={\varrho }_L\times \frac{V}{5}+{\varrho }_w\times \frac{4}{5}v$

${\varrho }_m=(\frac{13.5}{5}+\frac{4}{5})\times {10}^{3}kg/m^3$

${\varrho }_m=3.5\times {10}^{3}kg/m^3$