Question

A metallic sphere floats 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 $(4/5{)}^{th}$ portion is in water and $(1/5{)}^{th}$ portion is in the liquid. The density of the metal in $kg/m^3$ is

• A. $4.5\times {10}^3$
• B. $4.0\times {10}^3$
• C. $3.5\times {10}^3$
• D. $3.0\times {10}^3$

Answer 1

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

Acc. to archimedes principle

Mass sphere = displace mass (water + liquid)

$\rho v={\rho }_w\left(\frac{4v}{5}\right)+{\rho }_l\left(\frac{v}{5}\right)$

$\rho =\frac{4{\rho }_w}{5}+\frac{{\rho }_l}{5}$

$=\frac{4\times {10}^3+13.5\times {10}^3}{5}$

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

Answerl-$\left(c\right)$