Question

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

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

Answer 1

The correct option is C $7.2$

Let's take the density and volume of sphere be 's' and 'v' respectively.

So, the weight of the body$=svg$

Volume of sphere in oil$=\frac{v}{2}$

So, volume of oil displaced by sphere$=\frac{v}{2}$

So, buoyant force$\left(F_{bo}\right)$ due to oil$=s_o\frac{v}{2}g$

similarly, buoyant force, $\left(F_{bm}\right)$ due to mercury$=sm\frac{v}{2}g$

Since, the sphere is stationary, so

$svy=F_{bo}+F_{bm}$

$svg=s_o\frac{v}{2}g+s_m\frac{v}{2}g$

$\Rightarrow s=\frac{s_o+s_m}{2}=\frac{0.8+13.6}{2}=\frac{14.4}{2}$

$\Rightarrow s.\left(body\right)$=7.2g/cm^2$.