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27 July, 10:12

Imagine that the apparent weight of the crown in water is Wapparent=4.50N, and the actual weight is Wactual=5.00N. Is the crown made of pure (100%) gold? The density of water is rhow=1.00 grams per cubic centimeter. The density of gold is rhog=19.32 grams per cubic centimeter.

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  1. 27 July, 10:23
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    Actual weight, Wo = 5 N

    Apparent weight, W = 4.5 N

    density of water = 1 g/cm^3 = 1000 kg/m^3

    density of gold, = 19.32 g/cm^3 = 19.32 x 1000 kg/m^3

    Buoyant force = Actual weight - Apparent weight

    Volume x density of water x g = 5 - 4.5

    V x 1000 x 9.8 = 0.5

    V = 5.1 x 10^-6 m^3

    Weight of gold = Volume of gold x density of gold x gravity

    W' = 5.1 x 10^-6 x 19.32 x 1000 x 9.8 = 0.966 N

    As W' is less than W so, it is not pure gold.
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