Question

A body floats in water with one-third of its volume above the surface of water. If it is placed in oil, it floats with half of its volume above the surface of the oil. The relative density of the oil is

• A. $\frac{3}{4}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is C $\frac{4}{3}$

In water ,
$\frac{2}{3}V$ is below the surface of water,
$F_{Bw}=\frac{2}{3}V{\rho }_{w}g=mg......\left(1\right)$


In oil,
$\frac{1}{2}V$ is below the surface of oil.


$F_{Bo}=\frac{1}{2}V{\rho }_{o}g=mg......\left(2\right)$
We know,
$\text{Relative density of oil}=\frac{{\rho }_o}{{\rho }_w}$
From $\left(1\right)$ and $\left(2\right)$, we get
$\therefore \frac{{\rho }_o}{{\rho }_w}=\frac{4}{3}$