Question

A metal sphere floats in an immiscible mixture of water (density ${10}^{3}kg/m^3$) and a liquid of density $(13.5\times {10}^{3}kg/m^3)$ such that its ${\left(\frac{4}{5}\right)}^{th}$ portion is in water and ${\left(\frac{1}{5}\right)}^{th}$ portion in liquid.The density of metal is

• A. $7.25\times {10}^{3}kg/m^3$
• B. $3.5\times {10}^{3}kg/m^3$
• C. $\sqrt{13.5}\times {10}^{3}kg/m^3$
• D. $14.51kg/m^3$

Answer 1

Answer: (B)

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

$V\rho g=\frac{4}{5}V\times {10}^{3}g+\frac{1}{5}V\times 13.5\times {10}^{3}g$

$\Rightarrow \rho =\frac{4+13.4}{5}\times {10}^3=3.5\times {10}^{3}kg/m^3$