Question

A vessel contains oil (density = $0.8{\text{g/cm}}^3)$ over mercury (density = $13.6{\text{g/cm}}^3)$. A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in ${\text{g/cm}}^3$ is

• A. $3.3$
• B. $6.4$
• C. $7.2$
• D. $12.8$

Answer 1

The correct option is C $7.2$


As the sphere floats in the liquid, therefore its weight will be equal to the upthrust force on it.
Weight of sphere = $\frac{4}{3}\pi R^3\rho g$.......(i)
Upthrust due to oil and mercury,
$=\frac{2}{3}\pi R^3{\rho }_{\text{oil}}g+\frac{2}{3}\pi R^3{\rho }_{\text{Hg}}g$......(ii)
Equating (i) and (ii),
$\frac{4}{3}\pi R^3\rho g=\frac{2}{3}\pi R^3\left(0.8\right)g+\frac{2}{3}\pi R^3\left(13.6\right)g$
$\Rightarrow 2\rho =0.8+13.6=14.4\Rightarrow \rho =7.2{\text{g/cm}}^3$