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9 June, 12:18

An iron anchor of density 7810.00 kg/m^3 appears 252 N lighter in water than in air. (a) What is the volume of the anchor? (b) How much does it weigh in air?

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  1. 9 June, 12:34
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    (a) The volume of the iron anchor = 25.2 m³

    (b) The mass of iron = 196812 kg

    Explanation:

    Density: This is the ratio of the mass of a body to its volume. The S. I unit of density is kg/m³

    (a)

    From Archimedes principle, the iron will displace a volume of water that is equal to its volume. And the weight of water displaced is equal to loss in weight or upthrust.

    Therefore, Upthrust = lost in weight = weight of water displace.

    Therefore, Volume of the iron = mass of water displace/density of water

    Vi = m₁/D₁ ... Equation 1

    Where Vi = volume of iron, m₁ = mass of water displaced, D₁ = Density of water.

    Given: upthrust = 252 N, ∴ m₁ = 252/10 = 25.2 kg.

    Constant: D₁ = 1.0 kg/m³

    Substituting these values into equation 1,

    Vi = 25.2/1.0

    Vi = 25.2 m³

    Therefore the volume of the iron anchor = 25.2 m³

    (b)

    Density of the iron = mass of the iron/volume of the iron.

    Therefore, Mass of the iron = Density of the iron * volume of the iron ... equation 2

    Given: Density of the iron = 7810 kg/m³, Volume of the iron = 25.2 m³

    Substituting these values into equation 2,

    Mass of the iron = 7810*25.2

    Mass of the iron = 196812 kg.

    Therefore the mass of iron = 196812 kg
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