Question

Iceberg floats in sea water with a part of it submerged. The percentage fraction of the ice berg submerged is (Density of ice $= 0.9 \,g \,cm^{-3}$, density of sea water $= 1.1 g cm^{-3}$)

• A. $18\%$
• B. $12\%$
• C. $10\%$
• D. $8\%$

Answer 1

Answer: (A)

$V$ be the volume of the iceberg, $x$ be the volume out of sea water
The iceberg is floating in sea water then
$V \rho_{ice} g=\left(V-x\right) \rho_{sea\,water} g$
or $V\times0.9\times g=\left(V-x\right)1.1\,g $
or $0.9V =1.1 V-1.1 x$
$0.2 V =1.1 x$
$\therefore \frac{x}{V}=\frac{0.2}{1.1}$
Percentage of fraction of the volume of iceberg above thelevel of sea water
$\frac{x}{V}\times100=\frac{0.2}{1.1}\times100$
$=18\%$