Question

A vessel contains oil (density = 0.8 $gm/c{m}^3$) over mercury (density = 13.6 $gm/c{m}^3$). A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of sphere in $gm/c{m}^3$ is:

• A. 3.3
• B. 6.4
• C. 7.2
• D. 12.8

Answer 1

The correct option is C 7.2

In equilibrium, the weight of the sphere is equal to the sum of the buoyant forces.

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

$\therefore {\rho }_{sphere}=\frac{1}{2}({\rho }_{Hg}+{\rho }_{oil})=\frac{1}{2}(13.6+0.8)=7.2gmc{m}^{-3}$