Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold (density of gold is 19.3 × 103 kg/m3).

Question

Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold (density of gold is 19.3 × 103 kg/m3). According to legend, he solved this problem by weighing the crown first in air and then in water. Suppose the scale read 8.90 N when the crown was in air and 7.80 N when it was in water. Find the density. What should Archimedes have told the king?

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Thu Cúc 1 year 2021-08-02T05:59:07+00:00 1 Answers 10 views 0

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    2021-08-02T06:00:43+00:00

    Answer:

    Explanation:

    First, we can find the mass of the object in air

    Since W = mg

    m = W/g = (8.9)/(9.8) = 0.908 kg

    Then, by Archimedes principle, we can find its volume. The volume is found by the weight of the water displaced by the formula

    W = Vρg

    The Weight is the difference in scale readings. The density of water is 1000 kg/m3

    (8.9- 7.8) = V(1000)(9.8)

    Thus V = 1 X 10-4 m3

    Then, since density is mass / volume

    ρ = 0.908/1 X 10-4

    ρ = 8254 kg/m3 which is 8 X 103 kg/m3

    The density of gold is 19.3 X 103 kg/m3

    Since those densities are not the same, the crown is either hollow or not pure gold

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