Question

An iceberg is submerged partially in the sea and remaining 1/3 part is outside the sea level. Use Archimedes' principle to determine the density of an iceberg.

Answer 1

The weight of the iceberg is in equilibrium with the buoyant force:

$$F_g=F_A,\\ mg=F_a,\\ \rho_iV_ig=\rho_w gV_\text{submerged},\\ \rho_iV_ig=\rho_w g\bigg(1-\dfrac 13\bigg)V_i,\\ \rho _i=\dfrac 23 \rho_w=667\text{ kg/m}^3.$$