legend has it that Archimedes was asked by King Hiero of syracuse to determine w

Question

legend has it that Archimedes was asked by King Hiero of syracuse to determine wether a crown was of pure gold or had been adultered witha lesser metal by an unscrupulus goldsmith. It was this problem that led him to the principle that bears his name. In a modern version of this method, a crown weighing 8.30 N is suspended underwater from a string. The tension in the string is measured to be 7.81 N.

Is the crown pure gold? (the answer is no, the crown is not pure gold; can you explain in detail how to work this problem)

Explanation / Answer

density of gold p = 19320 kg/m^3

density of water pw = 1000 kg/m^3

weight of crown w = mg = pV*g

8.3 = 19320*V*9.8

Volume of crown V = 4.384*10^-5 m^3

According to Archomedes principle

loss of weight of crown in water = weight of displaced water

w -T = pw*V*g

8.3 - 7.81 = pw*4.384*10^-5*9.8

pw = 1140 kg/m^3

but density of water is 1000 kg/m^3.

So crown is not pure gold

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