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 the crown to be 1.47 kg. You then put a large beaker of water on the balance to 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, buyouncy force on crown = weight in air of crown - weight in water of crown

=>   volume * density of water   =   1.47 - 1.39

=>    volume * 1000 =   0.08

=>    volume of crown = 8 * 10-5 m3

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

                                    = 18375   kg/m3

But , Actual density of gold = 19300 kg/m3

=>    The crown is not gold as its density is less than gold .

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