Question

A vessel contains oil of density $0.8g/c{m}^3$ over mercury of density $13.6g/c{m}^3$. A homogeneous sphere floats with $\frac{1}{4}$ of its volume immersed in mercury and the rest $\frac{3}{4}$ in oil. The density of the material of the sphere is

• A. $5g/c{m}^3$
• B. $4g/c{m}^3$
• C. $2g/c{m}^3$
• D. $3g/c{m}^3$

Answer 1

The correct option is B $4g/c{m}^3$

Given, density of the mercury,

${\rho }_m=13.6g/c{m}^3$

Density of the oil, ${\rho }_{oil}=0.8g/c{m}^3$

As given $\frac{1}{4}$ volume of the vessel immersed in mercury and $\frac{3}{4}$ volume is in oil,

$\frac{V}{4}\times 13.6g+\frac{3V}{4}\times 0.8\times g=V\rho g$

$\rho =3.4+0.6=4g/c{m}^3$

Final answer : (c)