Hello students, you must have heard about famous story involving word, “Eureka! Eureka!!” Yes we are talking about very interesting concept which was studied and illustrated by Sir Archimedes.
Just think, if you have a container filled with water at edges, and a stone is dropped in it. You will observe that water will be spills out of the container. The question is by what amount water will come out of it? Is it equal to size of stone? Then is it equal to weight of stone? Any other parameter? Can you guess?
Answer of this was illustrated by Sir Archimedes in following experiment.
Consider a small beaker filled completely with water and kept in wide container so as to avoid loss of water after falling out of beaker. Now small stone of mass ‘m’ is dropped slowly into beaker as shown in fig.
When stone is dropped in small beaker, water surface exerts the buoyant force on it, reaction of this is recorded by observing the amount of water which is spills out of the beaker and collected in wide container as shown in fig. If we measure the weight of water collected in wide beaker that will be the buoyant force exerted by water on stone!
Then according to Archimedes principle, “if object is immersed in liquid completely or partially, the buoyant force exerted by liquid on an object is equal to weight of liquid which is displaced by the object”.
Consider a liquid is filled in container. Let,
ρ = density of liquid
m = mass of liquid which gets displaced
g = acceleration due to gravity at that point
V = volume of object immersed in liquid
Then the weight of liquid displaced is given as,
weight of liquid that gets displaced = mg ………. (1)
We know that,
Then, W = ρVg …………………………..(2)
As per Archimedes principle, this weight is nothing but the buoyant force hence,
∴ Buoyant force, F = ρVg …………..(3)
This is the formula for find buoyant force. Due to buoyancy the weight of object in liquid can be given as,
Weight of object in liquid (apparent weight) = Actual weight- buoyant force.
Following are some examples where Archimedes principle can be applied.
- A person can swim easily on free surface of water is due to the buoyant force exerted by water, which reduces the effective weight of person so that it can float on water surface.
- Heavy ships or boats can easily floats on the river/ocean surface due tremendous buoyant force exerted by ocean surface due to its large volume.
- Submarines used in Navy Force uses this principle, in which a tank filled with water is separately arranged with a piston. When we wish to float, piston pushes the water out of that tank so that the weight of submarine is less than that of buoyant force exerted by ocean water. If we want to hide under water, the tank is refilled with water so as to increase its weight and can sink below the surface of water.
Here are some numerical will help us to understand the concept in more details, so let’s learn them.
Ex:1) A container from a truck falls from bridge in to river water. The volume of container is 50000 litres. What is the magnitude of buoyant force exerted by river water on container? What is the apparent weight of container on water surface if it’s the total mass is 100,000 kg.
Volume of container= volume of water displaced= 50000 litre= 50 m3
Density of water= 1000 kg/m3
Acceleration due to gravity, g= 9.8 m/s2
According to Archimedes principle,
∴ Buoyant force, F = ρVg
∴ F = 1000 × 50 × 9.8
∴ F = 4,90,000 N
∴ F = 4.9 × 105 N
Now apparent weight of container is,
Weight of object in liquid (apparent weight) = Actual weight- buoyant force
= W- F
= mg- F
= 100000 × 9.8 – 4,90,000
= 9,80,000 – 4,90,000
= 4,90,000 N