Question

A solid body floating on water has one-fifth of its volume above the surface. It is allowed to float in a liquid of relative density $1.25$, the fraction of the volume that will above the surface of liquid is

• A. $\frac{16}{25}$
• B. $\frac{7}{25}$
• C. $\frac{4}{25}$
• D. $\frac{9}{25}$

Answer 1

The correct option is D $\frac{9}{25}$

In water

$\frac{4}{5}V$ is below the surface of water.
$F_{Bw}=\frac{4}{5}V{\rho }_{w}g=mg.....\left(i\right)$

In oil,

$xV$ is below the surface of oil.
$F_{Bl}=xV{\rho }_{l}g=mg......\left(ii\right)$

We know,
$\text{Relative density of liquid}=\frac{{\rho }_l}{{\rho }_w}=1.25$
So, from equation $\left(i\right)$ and $\left(ii\right)$,
$\frac{{\rho }_l}{{\rho }_w}=\frac{4}{5x}=1.25$
$\Rightarrow x=\frac{16}{25}$
$\therefore$ Fraction of volume of solid body above the surface of liquid is $\frac{9}{25}$