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21 September, 00:40

Suppose that a solid cube of some material floats on the surface of an oil puddle at a service station with 75.1 % of its volume submerged. The density of the oil is 923 kg/m 3. What is the density of the cube's material

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  1. 21 September, 04:14
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    Answer: density of material pm = 693.2kg/m^3

    Explanation:

    Using Archimedes principle.

    The buoyancy force equals the weight of material submerged which equals the weight liquid displaced.

    Fb = Wm = Wl

    I. e

    Wm = Wl

    pm. Vm. g = pl. Vl. g

    pm. Vm = pl. Vl

    pm/pl = Vl/Vm

    Where; pm and pl are the density of material and liquid oil respectively.

    Vm and Vl are the volume of material and volume liquid displaced respectively.

    g is the acceleration due to gravity

    Fb is the buoyancy force

    Wm and Wl are the material weight and liquid displaced weight respectively

    Given that the material displaced 75.1% of the volume of the liquid oil

    VI/Vm = 0.751

    pm/pl = 0.751

    pm = 0.751pl

    density of oil is 923kg/m^3

    pm = 0.751 * 923

    pm = 693.2kg/m^3
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