Question

An iceberg is floating partially immersed in sea water. The density of sea water $1.03gc{m}^{-3}$ and that of ice is $0.92gc{m}^{-3}$. The approximate percentage of total volume of iceberg above the level of sea water is

• A. $8$
• B. $11$
• C. $34$
• D. $89$

Answer 1

The correct option is B $11$

Density of iceberg $=0.92g/c{m}^3$

Density of water $=1.03gc{m}^{-3}$

Let volume submerged of iceberg in water $=V_s$ and total volume of ice $=V$

For floating condition -$F_b=mg$

$\left({\rho }_{water}\right)\left(V_s\right)\left(g\right)=\left({\rho }_{ice}\right)\left(V\right)g\frac{V_e}{V}=\frac{{\rho }_{ice}}{{\rho }_{water}}=\frac{0.92}{1.03}=\frac{92}{103}\frac{V_s}{V}=\frac{92}{103}$

Fraction of volume of ice submerged $=\frac{92}{103}$

Fraction of volume of ice which is outside water $=1-\frac{92}{103}=\frac{11}{103}$

$\%=\frac{11}{103}\times 100\approx 11\%$