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10 June, 10:23

You are trying to determine the specific gravity of a solid object that floats in water. If m is the mass of your object, mS is the apparent mass of the combination of 2 masses with one (the sinker) submerged, and mOS is the apparent mass of the combination of 2 masses with both submerged, what is the formula for specific gravity

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  1. 10 June, 10:30
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    Specific Gravity = m/[m (s) - m (os) ]

    Explanation:

    Specific gravity, also called relative density, is the ratio of the density of a substance to the density of a reference substance. By this definition we need to find out the ratio of density of the object of mass m to the density of the surrounding liquid.

    m = mass of the object

    Weight in air

    W (air) = mg, where g is the gravitational acceleration

    Weight with submerged with only one mass

    m (s) g + Fb = mg + m (b) g, consider this to be equation 1

    where Fb is the buoyancy force

    Weight with submerged with both masses

    m (os) g + Fb' = mg + m (b) g, consider this to be equation 2

    equation 1 - equation 2 would give us

    m (s) g - m (os) g = Fb' - Fb

    where Fb = D x V x g, where D is the density of the liquid the object is submerged in, g is the force of gravity and V is the submerged volume of the object

    m (s) g - m (os) g = D (l) x V x g

    m (s) - m (os) = D (l) x V

    we know that Mass = Density x V, which in our case would be, D (b) x V, which also means

    V = Mass/D (b), where D (b) is the density of the mass

    Substituting V into the above equation we get

    m (s) - m (os) = [D (l) x m) / D (b) ]

    Rearranging to get the ratio of density of object to the density of liquid

    D (b) / D (l) = m/[m (s) - m (os) ], where D (b) / D (l) denotes the specific gravity
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