It is said that Archimedes discovered his principle during a bath while thinking

Question

It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if King Hiero's crown was actually made of pure gold. While in the bathtub, he conceived the idea that he could determine the average density of an irregularly shaped object by weighing it in air and also in water. If the crown weighed 3.55 kgf (= 34.8 N) in air and 3.25 kgf (= 31.9 N) in water, determine if the crown is made of pure gold. The density of gold is 19, 300 kg/m^3 Discuss how you can solve this problem without weighing the crown in water but by using an ordinary bucket with no calibration for volume. You may weigh anything in air.

Explanation / Answer

1) Immerse the crown in bucket full of water. Some water will be displaced and overflowed.

2) Measure weight of the overfolwed water.

3) We know density of water and we can calculate volume of water from weight.( V = (34.8-31.9)/1000 == (34.8-31.9)/1000 = 0.0029 m^3

4) Volume of displaced water = volume of crown =V =

0.0029 m^3

5) Now calculate density of crown = 34.8/0.0029 =12000 kg/m^3

It is lower than density of pure gold => Crown is made of impure gold

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