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6 October, 22:27

A rectangular wooden block measures 10.0 cm * 4.00 cm * 2.00 cm. When the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. What is the density of the wood?

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  1. 6 October, 23:42
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    825 kgm⁻³

    Explanation:

    ρ = density of wood = ?

    ρ' = density of water = 1000 kgm⁻³

    V = volume of wood = 10 x 4 x 2 = 80 cm³ = 80 x 10⁻⁶ m³

    V' = Volume of water displaced = 10 x 4 x 1.65 = 66 cm³ = 66 x 10⁻⁶ m³

    Using equilibrium of force in vertical direction

    Force of buoyancy = Weight of the wood

    ρ' V' g = ρ V g

    ρ' V' = ρ V

    (1000) (66 x 10⁻⁶) = ρ (80 x 10⁻⁶)

    ρ = 825 kgm⁻³
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