Question

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

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

Answer 1

Answer: (B)

Let $V$ be the volume of iceberg and let $x$ be the fraction of volume above water.
Using law of floatation, weight of floating body = weight of liquid displaced by part of the floating body inside the liquid.
Therefore, $V \rho_{\text {ice }} g=(1-x) V \rho_{\text {water }} g$.
Using the value of $\rho_{\text {ice }}$ and $\rho_{\text {water }}$ we get $x=(13 / 103)$.