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A block of material with density $3 \mathrm{~g} / \mathrm{cc}$ is placed on a fluid of density $7 \mathrm{~g} / \mathrm{cc}$. The fraction of volume of the piece of material outside the fluid is
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The correct answer is:
0.57
Density of the material, $\rho=3 \mathrm{~g} / \mathrm{cc}$
Density of the fluid, $\sigma=7 \mathrm{~g} / \mathrm{cc}$
Let the volume of the material be $V$ and $n$ portion of the volume of the block submerged in the fluid.
$\therefore$ Weight of the fluid is $V \rho g$ and weight of the submerged part is $n V \sigma g$
According to the condition of equilibrium of a floating body.
$$
\begin{aligned}
V \rho g & =n V \sigma g \\
\Rightarrow \quad n & =\frac{\rho}{\sigma}=\frac{3}{7}
\end{aligned}
$$
$\therefore$ The fraction of volume of the block outside the fluid is $1-n=1-\frac{3}{7}=\frac{4}{7}=0.57$
Density of the fluid, $\sigma=7 \mathrm{~g} / \mathrm{cc}$
Let the volume of the material be $V$ and $n$ portion of the volume of the block submerged in the fluid.
$\therefore$ Weight of the fluid is $V \rho g$ and weight of the submerged part is $n V \sigma g$
According to the condition of equilibrium of a floating body.
$$
\begin{aligned}
V \rho g & =n V \sigma g \\
\Rightarrow \quad n & =\frac{\rho}{\sigma}=\frac{3}{7}
\end{aligned}
$$
$\therefore$ The fraction of volume of the block outside the fluid is $1-n=1-\frac{3}{7}=\frac{4}{7}=0.57$
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