Question

A vessel contains oil (density $=0.8g/{cm}^2$) over mercury (density $=13.6g/{cm}^3$). A homogenous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the 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 $7.2$

Let volume of space be $V$

According to Archimedes principle Buoyant free on ball $=$ weight

$($ Since ball is in equilibrium $)$

${\rho }_{b}V.g={\rho }_{oil}\frac{V}{2}.g+{\rho }_{mer}\frac{V}{2}g\Rightarrow {\rho }_b=\frac{{\rho }_{oil}+{\rho }_{mer}}{2}=\frac{0.8+13.6}{2}=\frac{14.4}{2}=7.2gc{m}^{-}3$