As your textbook indicates Archimedes was an ancient Greek philosopher. Accordin

Question

As your textbook indicates Archimedes was an ancient Greek philosopher. According to tradition, he discovered what has to be called Archimedes' Principle in the course of trying to solve a dilemma posed to him by King Hiero of Syracuse. King Hiero had provided pure gold to a goldsmith to fashion a crown. When the was finished, it had the same mass as the king had supplied. Nonetheless, the king suspected that the goldsmith had stolen some of the gold. The king believed the goldsmith has mixed a cheaper metal, silver, into the crown to replace the gold he had taken. The king asked Archimedes to analyze the crown and determine if the goldsmith had cheated. Archimedes knew that silver was less dense than gold. He, there, asked for a mass of gold equal to the to the of the crown. He then put the gold in a container, filled the container to the brim with water, and removed the gold. (A) What happened to the water level in the container when the gold was removed? Why? (B) Archimedes then took the crown fashioned by the goldsmith and carefully lowered it into the container water. What should have happened to the water level if the crown had been made of pure gold? (c) When Archimedes lowered the crown into the container, the water overflowed. What did this indicate about the volume of the crown compared to the volume of the mass of gold? Did this prove or disprove that the goldsmith had cheated the King? Why?

Explanation / Answer

A) When the gold was removed, the water level in the container went down because the gold was taking some space and when it was removed, that space was left for water and so the level comes down.

B) Had the crown been made of pure gold, it would have replaced the same amount of water from the tank and the level in the tank would have gone upto the the same mark as previously with pure gold inside the water tank. Because any material dispalces the water equivalent to its volume, and its weight inside the water is balanced by weight of the water displaced.

C) So when Archimedes lowered the crown into the container, the water overflowed because the volume of the crown was more than the volume the crown if it was made of pure gold. But since some silver was also mixed in the crown, and silver is less denser than gold, so same mass of silver will have greater volume than that of gold.

So, this proves that smith had cheated the king, because if the crown was made of pure gold, the level in the container would not have been overflowed due the same volume of gold, but since silver was mixed so volume became more and water overflowed.

I hope I explained you well.

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