Question

A vessel contains oil (density $=0.8gm/c{m}^3$ ) over mercury ( density $=13.6gm/c{m}^3$ ). $A$ 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 $gm/c{m}^3$ is

• A. 3.3
• B. 6.4
• C. 7.2
• D. 12.8

Answer 1

Answer: (C)

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