Question

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is

${\rho }_i=0.917\frac{g}{c{m}^3}?$

Answer 1

Given,

Density of ice is ${\rho }_i=0.917\frac{g}{c{m}^3}$

Let the density of water be ${\rho }_w=1\frac{gm}{c{m}^3}.$

Let the volume of the iceberg be $V.$

Weight of the iceberg

$W={\rho }_{i}gV$ .....$\left(i\right)$


$x$ is the fraction of iceberg submerged in water, then the volume of water
displaced:

$V_s=xV$

Buoyant force due to submerged part of iceberg

$F_B={\rho }_{w}g{V}_3$

At equilibrium:

$F_B=W$

${\rho }_{w}g{V}_s={\rho }_{i}gV$

${\rho }_{w}g\left(xV\right)=p_{i}gV$

$x=\frac{{\rho }_i}{{\rho }_w}=\frac{0.917}{1}$

$x=0.917$

Final Answer$:0.917$