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Let’s assume that Hiero, the ruler of ancient Syracuse, gave his goldsmith 10.00 N of pure gold to make a crown. Indeed, the crown weighed 10.00 N when in air, but Hiero suspected that some of the gold was replaced by silver. Archimedes weighed the crown fully immersed in water and found that it appeared to weigh 9.37 N. How much should the crown have weighed under water, if it were made of pure gold? As this was not the case, how much gold was replaced by silver? The specific gravity of gold is 19.3 and that of silver is 10.5.

Hint: Find the volume of the crown.


Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from The Baldwin Project.

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