Archimedes discovered the concepts leading to Archimedes' Principle one day when stepping into the bath. He noticed that the more of his body was in the water, the higher the water level rose. At the time, the king was trying to determine whether his crown was made of solid gold or if it actually contained some silver.
(1) Explain how Archimedes could use his new discoveries to determine if the king's crown was gold or if he had been cheated by the craftsmen who had made it.
Archimedes' Principle states that a submerged body experiences a buoyant force of magnitude equal to the weight of the fluid displaced. If the gold in the crown had been replaced with silver, a less dense metal, the crown would weigh less (the crown would have less mass per unit volume but the same volume, so it would have less mass and less weight), and the buoyant force required to make the crown float would be less. Floating the crown in a fluid in which a crown of gold would sink but a crown of silver would float should therefore determine whether the king had been cheated (in this case, he had).
