Introduction To Archimedes Principle

If you submerge any solid object in water, it appears to lose weight. If we go swimming, we also feel little weightless in the water. The reason for this is that liquids exert an upward force to objects submerged in them. This is known as thrust and is a consequence of the difference in pressure a liquid exerts at different heights. As we submerge an object (Considering it is fully submerged) deeper into a liquid, the pressure exerted by the liquid keeps on increasing but the thrust force does not increase.

The value of this thrust force is given by the Archimedes principle which was discovered by Archimedes of Syracuse of Greece.
When an object is partially or fully immersed in a liquid, the apparent loss of weight is equal to the weight of liquid displaced by it.

Archimedes Principle

If you look at the figure, the weight due to gravity is opposed by the thrust provided by the fluid. The object inside the liquid only feels the total force acting on it as the weight. Because the actual gravitational force is decreased by the liquid’s upthrust, the object feels as though its weight is reduced. The apparent weight is thus given by:

Apparent weight= Weight of object (in air) – Thrust force (buoyancy)

Archimedes principle tells us that this loss of weight is equal to the weight of liquid the object displaces. If the object has a volume of V, then it displaces a volume V of the liquid when it is fully submerged. If only a part of the volume is submerged, the object can only displace that much of liquid.

Archimedes principle equation

The mass of the liquid displaced is.

\(Mass\) = \(Density~ × ~Volume\) = \(ρ~×~V\)

This is because density (ρ) is defined as

\(Density,ρ\) = \(\frac{Mass}{Volume}\) = \(\frac{M}{V}\)

Thus the weight of that displaced liquid is:

\(Weight\) = \(Mass~ ×~ Acceleration~ due~ to~ gravity\)

\(W\) = \(M~×~g\) = \(ρ~×~V~×~g\)

Thus from Archimedes principle, we can write:

Apparent loss of weight = weight of water displaced = ρ×V×g

Thus the Thrust force is,

\(Thrust\) = \(ρ~×~V~×~g\)

Where, \(ρ\) = density of liquid

\(V\) = volume of liquid displaced

The thrust force is also called the buoyant force because it is responsible for objects to float. Thus, this equation is also called the law of buoyancy.

You can try an Archimedes principle experiment at home. Take a mug filled with water to the brim and place it in an empty bowl. Now take any solid object you like and measure its weight using a spring balance. Note this down. Keep the object attached to the spring balance and submerge it in the water. Just make sure the spring balance is not submerged. Now, note down the weight shown by the spring balance. You will notice that it is less. Some water will be displaced into the bowl. Collect this water and weigh it. You will find that the weight of water will be exactly equal to the loss of weight of the object!

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Practise This Question

Consider two point masses separated by a particular distance. Now, if the masses are tripled, and the distance of separation is also tripled, then what will happen to the gravitational force between them?