Archimedes\' gold crown. Archimedes didn\'t have an electronic balance, but for

Question

Archimedes' gold crown. Archimedes didn't have an electronic balance, but for this problem, let's assume he had one. (He did use a method similar to the one in this problem to check up on the king's goldsmith.) Pretending you are Archimedes, you find the mass of a crown to be 1.47 kg. You then put a large beaker of water on the balance and tare it (meaning you set the scale to read zero with the water on it). With the gold crown hanging from a string, you completely submerge the crown in the water without letting it touch the bottom or sides of the beaker. The balance now reads 1.39 kg. Because the crown is weighty, dense, and gold-colored, it looks like gold. Is it gold? What will you tell the king?

Explanation / Answer

Here,

mass of crown , m = 1.47 Kg

as the reading reduced on the scale due to mass of displaced water

mass of displaced water , m1 = 1.47 - 1.39 Kg

m1 = 0.08 Kg

volume of crown = m1/density of water

volume of crown = 0.08/(1000) m^3

volume of crown = 8 *10^-5 m^3

density of crown = m/V

density of crown = 1.47/(8 *10^-5)

density of crown = 18375 Kg/m^3

as density of gold = 19320 Kg/m^3

this is NOT pure gold

wle should tell the king , crown is not pure gold

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