Physics - Fluid Question with Solution | TestHub

Let the total volume of the sphere be $V$ and its density be $\rho$.

The sphere is in equilibrium, so its weight is balanced by the total buoyant force exerted by the two liquids.

Weight of the sphere $=V\rho g$

Buoyant force due to mercury $=\frac{V}{2}{\rho }_{Hg}g$

Buoyant force due to oil $=\frac{V}{2}{\rho }_{oil}g$

Equating the weight to the total buoyant force:

$V\rho g=\frac{V}{2}{\rho }_{Hg}g+\frac{V}{2}{\rho }_{oil}g$

$\rho =\frac{{\rho }_{Hg}+{\rho }_{oil}}{2}$

Substituting the given values, ${\rho }_{Hg}=13.6$ g/cm${}^3$ and ${\rho }_{oil}=0.6$ g/cm${}^3$:

$\rho =\frac{13.6+0.6}{2}$

$\rho =\frac{14.2}{2}=7.1$ g/cm${}^3$

Answer: $7.1$