Question

A vessel contains oil (density $0.9 \, g \, cc^{- 1}$ ) over mercury (density $13.6 \, g \, cc^{- 1}$ ). A homogeneous sphere floats with one-third of its volume immersed in mercury and the rest immersed in oil. The density of the material of the sphere in $g \, cc^{- 1}$ is

• A. $3.3$
• B. $6.4$
• C. $5\text{.1}$
• D. $12.8$

Answer 1

Answer: (C)

For equilibrium, the total upward push will be equal to the downward pull. If $V$ is the volume of the sphere, then we have
$\left(\frac{V }{3}\right)\left(1 3 \text{.} 6\right)\text{g}+\left(\frac{2 V ⁡}{3}\right)\left(0 \text{.9}\right)\text{g}=V⁡\rho \text{g}$
$\therefore \rho =\left(\frac{1 3 \text{.} 6 + 1 \text{.} 8}{2}\right)\left(\text{g cm}\right)^{- 3}=5\text{.1}\left(\text{g cm}\right)^{- 3}$