Question

The density of ice is $920kg/m^3$, and that of sea water is $1030kg/m^3$. What fraction of the total volume of an iceberg is outside the water?

• A. $0.107$
• B. $0.207$
• C. $0.307$
• D. $0.407$

Answer 1

Answer: (A)

$0.107$

Let $V_L$ and $V_S$ be the volume of water displaced and volume of the ice respectively; ${\rho }_L$ and ${\rho }_S$ be the density of water and density of ice respectively. Since ice is floating on water, $F_B=W$
or ${\rho }_L{V}_{L}g={\rho }_S{V}_{S}g$ or ${\rho }_L{V}_L={\rho }_S{V}_S$
or $\frac{V_L}{V_S}=\frac{{\rho }_S}{{\rho }_L}$
This is the fraction of volume of the iceberg that is inside the water. Therefore, the fraction of volume of the iceberg that is outside the water is given by, 1 - 0.893 = 0.107
Hence, the fraction of the total volume of an iceberg is outside the water is 0.107.