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25 January, 15:11

A metal object is suspended from a spring scale. The scale reads 930 N when the object is suspended in air, and 731 N when the object is completely submerged in water. Find the volume of the object. The acceleration of gravity is 9.8 m/s 2. Answer in units of m3.

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  1. 25 January, 15:46
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    The volume of the object = 0.0203 m³

    Explanation:

    From Archimedes principle,

    Upthrust = lost in weight = amount of water displaced.

    U = W₁ - W₂

    Where U = upthrust, W₁ = Weight in air, W₂ = weight in water.

    U = 930 - 731

    U = 199 N.

    but mass of water displaced,

    m = U/g where g = 9.8 m/s²

    m = 199/9.8

    m = 20.31 kg.

    Recall,

    Density = mass/volume.

    Density of water = mass of water displaced / volume of water displaced

    D = m/V

    V = m/D ... Equation 1

    Where V = volume of water displaced, m = 20.31 kg, D = 1000 kg/m³

    Substitute into equation 1

    V = 20.31/1000

    V = 0.0203 m³

    the volume of water displaced = 0.0203 m³

    Note: That when an object is immersed in water, the volume of water it displaced is equal to it's volume.

    Hence, Volume of water displaced = volume of the object.

    Hence the volume of the object = 0.0203 m³
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