Everyday Physics

Archimedes Principle


Archimedes of Syracuse was a smart man in the court of the king of Syracuse. Once, the king posed a problem to Archimedes. The king had been given a crown by an artisan who claimed that it was made of pure gold. The king did not trust this artisan and asked Archimedes to find out a way to check whether this was true.

Legend has it that Archimedes while bathing had his “eureka” moment and noticed that he could calculate the volume of a body based on volume of water displaced. Archimedes conducted a very simple experiment: he took a gold bar of equal weight as the crown and dumped it into water and noted the increase in height of the water,  he then dumped the crown into the same jar and noted change again.  As the story goes water displaced was higher and hence crown was made of Silver mixed with Gold. Archimedes is known to have run to the court of the king straight from the bath with his finding.

Archimedes’ Principle is thus stated as:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

What this fundamentally means is that the volume of water that is displaced is same as the volume of the object that is placed in the water.

Volume displaced = Volume of object

But the Volume = Density X Mass



And this volume of water that has been displaced is responsible for the force mentioned in the theorem.

As an analogy think about a packed elevator. Assume that the elevator cannot hold any more people. The elevator stops at a floor and some people are waiting to get in. These people obviously cannot get into the lift unless someone inside gets out. This is what happens when the object is submerged in the water as some water needs to move out for the object to occupy the space.


  • Archimedes of Syracuse was a Greek Philosopher, Mathematician and Scientist who lived between 287 and 212 B.C.E.

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