King heiro had provided pure gold to a goldsmith to fashion a crown.when the crown was finished, it had the same mass as the gold the king had supplied. Nonetheless, the king suspected that the goldsmith had stolen some of the gold. The king belived the goldsmith had mixed a cheaper metal,silver into the crown to replace the gold had taken. The king asked Archiemeds to analyze the crown and determine if the goldsmith had cheated . Archimedes knew that silver was less dense than gold.he therefore, asked for mass of gold equal to the mass of the crown.he then put the gold in a container, filled the container to the brim with and removed the gold. (A)what happened to the water level in the container when the gold was removed (b)Archimedes then took the crown fashioned by the goldsmith and cartefully lowered it into the container of water.what should have happened ti rhge 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 he crown compared to the volume of the mass of gold?Did this prove or disprove that the goldsmith had cheated the king ? why?
This is the famous experiment of Archemedes to test the purity of the golden crown.
Any substance when fully submerged in water displaces equal volume of water.
A) The water level was upto the brim when the crown was immersed in it. When it is removed, the water level should come down to a certain lower level. Difference in level from the brim indicating the volume of the crown.
B) Had the crown been made of pure gold, being of the same mass, it would have of the same volume, and the water level would have come to exactly the same level. Neither any overflow, nor any shortfall would have been observed.
C) When Archimedes lowered the crown into the container, the water overflowed. This indicates that the volume of the crown is greater than the mass of gold. Being of same mass, indicates that the material of the crown must be of lower density. Thus he came to the conclusion that the crown was an alloy of gold and a cheaper metal, such as silver, which was less dense than gold and therefore the crown had occupied more volume. Hence the goldsmith must have cheated the king.