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Q.
An ice- berg of density $900 \,kgm^{-3}$ is floating in water of density $1000 \,kgm^{-3}$. The percentage of volume of ice-berg outside the water is
AFMCAFMC 2010
Solution:
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 $V_{\text {in }} \sigma g=V \rho g$
$\Rightarrow V_{\text {in }}=\left(\frac{\rho}{\sigma}\right) V [\sigma=\text { density of water }]$
$\Rightarrow V_{\text {out }}=V-V_{\text {in }}=\left[\frac{\sigma-\rho}{\sigma}\right] V$
$ \Rightarrow \frac{V_{\text {out }}}{V} =\left[\frac{\sigma-\rho}{\sigma}\right] $
$=\frac{1000-900}{1000}=\frac{1}{10} $
$ \therefore V_{\text {out }} =10 \%$ of $ V$