Question

An iceberg is floating partially immersed in seawater. The density of seawater is $1.03gc{m}^{-3}$ and that of ice is $0.92gc{m}^{-3}$. The approximate percentage of the total volume of the iceberg above the level of seawater is

• A. $8$
• B. $11$
• C. $34$
• D. $89$

Answer 1

The correct option is B $11$

Let
$V$ is the total volume of the iceberg,
$\Delta V$ be volume of iceberg above sea level and
$V-\Delta V$ be the volume of submerged part of iceberg.
Then according to Archimedes principle, we have

weight of the water displaced (weight of $V-\Delta V$ volume of water)=weight of the iceberg
$(V-\Delta V)\times {\rho }_w\times g=V\times {\rho }_i\times g$
$(V-\Delta V)\times 1.03\times g=V\times 0.92\times g$

$\frac{V-\Delta V}{V}=\frac{0.92}{1.03}$

$\frac{\Delta V}{V}=1-\frac{0.92}{1.03}=\frac{0.11}{1.03}$
$\frac{\Delta V}{V}\times 100=\frac{11}{1.03}=11\%$