Question

A metallic sphere floats in an immiscible mixture of water $(w={10}^{3}kg/m^3)$ and a liquid $(L=13.5103kg/m^3)$ such that $\frac{4}{5}$ portion is in water and $\frac{1}{5}$th portion is in the liquid. The density of the metal in $kg/m^3$ is

• A. $4.5\times {10}^3$
• B. $4\times {10}^3$
• C. $3.5\times {10}^3$
• D. $3\times {10}^3$

Answer 1

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

Density of water $w={10}^{3}kg/m^3$

Density of liquid $L=13.5103kg/m^3$

Bouyant force $F=$ weight of water displaced + weight of liquid displaced

$\Rightarrow F=\frac{4}{5}Vwg+\frac{1}{5}LVg=Vdg$ $(d=\text{density of metal})$

$\Rightarrow \frac{4}{5}w+\frac{1}{5}L=d$

$\Rightarrow \frac{4}{5}\times {10}^3+\frac{1}{5}\times 13.5103=d$

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