Question

An iceberg is floating in an ocean. What fraction of its volume is above the water? (Given: density of ice$=900{\text{kg/m}}^3$ and density of ocean water $=1030{\text{kg/m}}^3$)

• A. $\frac{90}{103}$
• B. $\frac{13}{103}$
• C. $\frac{10}{103}$
• D. $\frac{1}{103}$

Answer 1

The correct option is B $\frac{13}{103}$

Let $V$ be the volume of iceberg and let $x$ be the fraction of volume above water.
Using law of floatation,
Weight of the floating body = Weight of liquid displaced by part of the floating body inside the liquid.

Therefore, $V{\rho }_{ice}g=(1-x)V{\rho }_{water}g$
Using the value of ${\rho }_{ice}$ and ${\rho }_{water},$ we get
$(1-x)=\frac{900}{1030}$
$\Rightarrow x=\frac{13}{103}$