Archimedes' principle was being stated when Archimedes of Syracuse tested the crown of King Hieron II. The crown has a mass of 13.4 kg but when submerged in water, an accurate scale reads only 12.1 kg. Is the king's crown made of gold?
Added by Stephen W.
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This principle can be used to determine the density of the material of the crown. Show more…
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Adi S.
Archimedes purportedly used his principle to verify that the king's crown was pure gold by weighing the crown submerged in water. Suppose the crown's actual weight was $25.0 \mathrm{~N}$. What would be its apparent weight if it were made of (a) pure gold and (b) $75 \%$ gold and $25 \%$ silver, by volume? The densities of gold, silver, and water are $19.3 \mathrm{~g} / \mathrm{cm}^{3}, 10.5 \mathrm{~g} / \mathrm{cm}^{3},$ and $1.00 \mathrm{~g} / \mathrm{cm}^{3},$ respectively.
Supreeta N.
In the third century $\mathrm{BC}$, the Greek mathematician Archimedes is said to have discovered an important principle that is useful in density determinations. The story told is that King Hiero of Syracuse (in Sicily) asked Archimedes to verify that an ornate crown made for him by a goldsmith consisted of pure gold and not a gold-silver alloy. Archimedes had to do this, of course, without damaging the crown in any way. Describe how Archimedes did this, or if you don't know the rest of the story, rediscover Archimedes's principle and explain how it can be used to settle the question.
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