In his “Treatise on floating” Archimedes Said:-

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.

The story goes that the king of Syracuse had given some gold to a goldsmith to produce a ceremonial crown forOpens the whole cartoon story in a new window use in religious ceremonies in the local temple, but he thought the goldsmith might have cheated by replaced some of the gold with an equal weight of silver.  So he set Archimedes (Top engineer of the day) the challenge of finding out, but without damaging the crown.

Now, silver is much lighter than gold, so if the crown had silver in it, it would have a greater volume than the same weight of gold. Then one day, while he was taking a bath, he was inspired to come up with this principle. He got so excited that he ran around Syracuse with no clothes on shouting, “Eureka” which more or less means “Got it”.

Archimedes had worked out that, if he took a balance scale and put the crown on one side and an equal weight of gold on the other it would balance until he put it under water. At that point, if the crown had a greater volume than the gold it would displace more water and experience a greater buoyant force, so the scales would become unbalanced. By replacing some of the gold with silver, the scales could then be made to balance, showing exactly how much the goldsmith had pilfered.

Of course, the principle applies to objects that are only partially immersed in water too. So, if the weight of an object is less than the water it would displace if completely immersed, it floats because the buoyant force it experiences is as great as its own weight.