Question

A metallic sphere floats in immiscible mixture of water (density ${10}^{3}kg/m^3$) and a liquid (density $8\times {10}^{3}kg/m^3$) such that its $\left(2/3\right)$ part is in water and $\left(1/3\right)$ part in the liquid. The density of the metal is

• A. $\frac{5000}{3}kg/m^3$
• B. $\frac{10000}{3}kg/m^3$
• C. $5000kg/m^3$
• D. $2000kg/m^3$

Answer 1

The correct option is B $\frac{10000}{3}kg/m^3$

Let the density of sphere be $P$.

Now,

on balancing forces on metallic sphere

$Mg=\frac{V}{3}(8\times {10}^3)\times 10+\frac{2V}{3}\times {10}^3\times 10$

Mass of sphere $=VP$

$VP\times 10=\frac{V}{3}(8\times {10}^3)\times 10+\frac{2V}{3}\times {10}^3\times 10$

$P=(\frac{8}{3}+\frac{2}{3})\times {10}^3$

$P=\frac{10}{3}\times {10}^3=\frac{10000}{3}Kg/m^3$