Archimedes of Syracuse states that:
“When an object is wholly or partially immersed in a fluid, then an upthrust acts on the object which is equal to the weight of liquid displaced by the object.”
Upthrust: It is defined as the force with which an object is pushed in an upward direction when it is immersed in a liquid. It is also called buoyancy or buoyant force.
In simple words, it states that when an object is immersed in a liquid, then the buoyancy acting on the object will be equal to the weight of the fluid displaced by the object; i.e. density multiplied by submerged volume times the gravitational constant g. Thus objects with greater mass and volume will have more buoyancy.
Loss of weight or apparent weight can be found by the following formula:
Loss of weight = weight in air – weight in water.
This is because the weight of any object is less in water than in air.
Application in submarines:
Submarines are designed in such a way that they can either float on the surface of water or submerge in it. In submarines, there are tanks which can be filled with water. To submerge the submarine in water, then its tanks are filled with water. The weight of the submarine becomes more than the weight of water displaced by it, thus it is submerged in the sea. In order to bring the submerged submarine back onto the sea surface again, the water from the tanks is pumped out.
A legend describes the discovery of the famous Archimedes’ principle as follows:
Archimedes stepped into a bath full of water. As soon as he stepped into it, a sizable amount of water was displaced. Archimedes realized that the amount of water displaced was equal to the buoyant force. He was so excited by this discovery that he ran naked down the street shouting Eureka!
Another legend says that:
King Heiron II suspected that the gold crown he had ordered was partly made of silver. Archimedes uncovered this fraud by using the Archimedes principle. He immersed two pieces of pure gold and silver equal to the weight of the crown and the crown itself in water. He found that the crown displaced more water than gold, but less water than silver, therefore concluding that the crown was made of another metal that was less dense than gold.
Step # 1: Suspend objects of different sizes and masses from a spring scale and note the readings of all the objects in air. After that, note the level of the water in the beaker.
Step # 2: Immerse the objects in the beaker of water and note the new reading in water of the objects.
Step # 3: Calculate the weight of water displaced by the objects.