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An ice-berg of density $900 \mathrm{kgm}^{-3}$ is floating in water of density $1000 \mathrm{kgm}^{-3}$. The percentage of volume of ice-berg outside the water is
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$10\%$
Let the volume of ice-berg is $V$ and its density is $\rho$. If this ice-berg floats in water with volume $V_{\text {in }}$ inside it then $V_{\text {in }} \sigma g=V \rho g$
$\Rightarrow V_{\text {in }}=\left(\frac{\rho}{\sigma}\right) V$
$\begin{aligned} \Rightarrow V_{\text {out }} & =V-V_{\text {in }}=\left(\frac{\sigma-\rho}{\sigma}\right) V \\ & =\left(\frac{1000-900}{1000}\right) V=\frac{V}{10} \\ \Rightarrow \frac{V_{\text {out }}}{V} & =0 \cdot 1=10 \%\end{aligned}$
$\Rightarrow V_{\text {in }}=\left(\frac{\rho}{\sigma}\right) V$
$\begin{aligned} \Rightarrow V_{\text {out }} & =V-V_{\text {in }}=\left(\frac{\sigma-\rho}{\sigma}\right) V \\ & =\left(\frac{1000-900}{1000}\right) V=\frac{V}{10} \\ \Rightarrow \frac{V_{\text {out }}}{V} & =0 \cdot 1=10 \%\end{aligned}$
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