The story of Archimedes running on the streets shouting ‘eureka’ is so popular that the word ‘eureka’ is frequently associated with any outstanding discovery made in science. But what is the astounding discovery he made that drove him into elation, if not craziness? Archimedes was confronted with a problem to figure out if a gold crown is adulterated with silver. The challenge was that the gold crown should not be tampered during the process. And the cause of his elation is, as understood, his solving the mystery. But how did he manage to do it without tampering with the crown?

Density of a material is a measure of its purity i.e., any kind of adulteration is associated with a change in density. Density is a physical quantity and it is defined as the mass of an object per unit volume of the object. So if one knows both mass and volume of an object one can measure the density and since density changes upon adulteration its easy to prove the same once density is measured. The mass of an object is easy to measure, as we all know. But how does one measure the volume of an object? Especially when the object is irregular in shape. The problem Archimedes faced boils down to measuring the volume of the object.

While taking bath, Archimedes realized that water level in the tub went up as he entered it. This gave him a clue to solve the mystery and as he figured it out he was elated and ran in the streets shouting Eureka. The concept he was enlightened to is now known as Archimedes’ Principle, and the related keyword often taught during our Physics Tuition classes is “Upthrust”. Water is incompressible is a fact known back then. In a gas there is a lot of empty space available and hence it is possible to compress gases where as the molecules in the liquids are so compactly arranged that any further compression is next to impossible. So when an object of certain volume is immersed in water, the object occupies the space, which was earlier occupied by water. The water molecules thus dispersed push the other water molecules in search for space eventually leading to the rise in water level. More importantly the rise in the water level is corresponds to the volume of object. So, if water is taken in a cylindrical vessel and the object is immersed in it, water level rises. The increase in the water level (w) can measured and where ‘r’ is the radius of the cylinder.

Archimedes used the same method to find out the volume of the crown. The mass of the crown can be measured by several methods. The density of the crown would then be mass of the crown divided by its volume. As we have discussed earlier the density of the crown will be equal to that of the density of gold if the crown is made of pure gold. Any change in the density of crown suggests adulteration and in fact it was found that the crown’s density was not same as that of gold and it is due to addition of silver.