an ice cube of density 0.9g/cm3floats in fresh water of density 1g/cm³ what fraction of volume of ice is submerged?

9/10

Explanation:

From Archimedes' principle, the buoyant force on the ice equals the weight of water displaced. Since the buoyant force equals the weight of the ice. then

ρ₁V₁g = ρ₂V₂g where ρ₁ = density of ice = 0.9 g/cm³ and V₁ = volume of ice and ρ₂ = density of water = 1 g/cm³ and V₂ = volume of water.

So. ρ₁V₁ = ρ₂V₂

V₁ = ρ₂V₂/ρ₁

=  1 g/cm³V₂/0.9 g/cm³ = 10V₂/9

Now, let x be the fraction of volume of ice submerged. So V = xV₁ = volume submerged. This volume also equals the volume of water since the submerged ice displaces its own volume of water.

So V = V₂

xV₁ = V₂

x(10V₂/9) = V₂

10x/9 = 1

x = 9/10