A piece of wood of uniform cylindrical cross section floats upright in a liquid of relative density 0.80 with 1/6 of its height above the liquid. If placed in water, what is the fraction of its height above the water level?

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  1. volume of wood = V
    density of wood = rhowood
    density of liquid = .8 * rho water = 800 kg/m^3
    density of water = 1000 kg/m^3

    in liquid
    rhowood * g * V = (5/6) * 800 *g * V
    rhowood = 5 *800 / 6 = 2000/3 = 2/3 * density of water
    so 1/3 of the wood is out of water

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