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15 December, 12:17

An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 16.5 N. When completely submerged in water, its apparent weight is 13.3 N. What is the volume of the object?

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  1. 15 December, 12:36
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    V = 1.7 x 10^{-3} m^{3}

    Explanation:

    apparent weight in ethyl alcohol = 16.5 N

    apparent weight in water = 13.3 N

    apparent weight = mg - ρgV

    where

    m = mass

    g = acceleration due to gravity = 9.8 m/s^{2}

    ρ = density

    V = volume

    for ethyl alcohol 16.5 = mg - ρ₁gV ... equation 1 for water 13.3 = mg - ρ₂gV ... equation 2

    we can solve the two equations above as simultaneous equations by subtracting equation 2 from equation 1

    we have

    16.5 - 13.3 = (mg - mg) - ρ₁gV - (-ρ₂gV)

    3.2 = gV (ρ₂ - ρ₁)

    V = / frac{3.2}{g (ρ₂-ρ₁) }

    where

    ρ₂ = density of water = 1000 kg/m^{3}

    ρ₁ = density of ethyl alcohol = 806 kg/m^{3}

    V = / frac{3.2}{9.8 (1000 - 806) }

    V = 1.7 x 10^{-3} m^{3}
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