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29 July, 11:20

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

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  1. 29 July, 11:33
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    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
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