Question

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

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

Answer 1

The correct option is C $7.2$

By Archimedes principle,

$\rho \gamma g={\rho }_0\frac{\gamma }{2}g+{\rho }_m\frac{\gamma }{2}$

$\rho =\frac{{\rho }_0}{2}+\frac{{\rho }_m}{2}$

$\because {\rho }_m=$density of mercury

${\rho }_0=$density of oil

$\rho =$density of material

$\rho =\frac{{\rho }_0}{2}+\frac{{\rho }_m}{2}$

$=\frac{13.6+0.8}{2}$

$\rho =7.2ℊ/㎤$