Question

An ice- berg of density $900kg{m}^{-3}$ is floating in water of density $1000kg{m}^{-3}$. The percentage of volume of ice-berg outside the water is

• A. 20%
• B. 35%
• C. 10%
• D. 11%

Answer 1

Answer: (C)

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 $V$