Question

An iceberg of density $900kg/m3$ is floating in water of density $1000kg/m3$. the percentage of volume of ice-cube outside the water is

• A. $10$ percent
• B. $20$ percent
• C. $31$ percent
• D. none of the above

Answer 1

Answer: (A)

$10$ percent

Let V is the total volume of iceberg

$V_{sub}$ = volume of iceberg submerged

${\rho }_b$= density of iceberg = 900 Kg/m3

${\rho }_w$= density of water = 1000 Kg/m3

So, for the flotation of body,

weight of body= weight of water displaced

$\Rightarrow {\rho }_{b}V={\rho }_w{V}_{sub}$

$\Rightarrow \frac{V_{sub}}{V}=\frac{{\rho }_b}{{\rho }_w}$

substracting both side from 1, we get

$\Rightarrow 1-\frac{V_{sub}}{V}=1-\frac{{\rho }_b}{{\rho }_w}$

$\Rightarrow \frac{V-V_{sub}}{V}=\frac{{\rho }_w-{\rho }_b}{{\rho }_w}$

Converting it in percentage,

$\Rightarrow \frac{V-V_{sub}}{V}\times 100=\frac{{\rho }_w-{\rho }_b}{{\rho }_w}\times 100$

by substituting values, we get

percentage volume outside the water= $\frac{1000-900}{1000}\times 100=10$%