Archimedes PrincipleTake a spring balance, a piece of stone, a measuring cylinder and water. Measure the weight of stone in air by tying the string around in a loop, and hanging it from the spring balance. Take water in a measuring cylinder and note its volume level. Then dip the stone in the water while it is still hanging from the spring balance. You will see that the stone is weighing less!! If you see the water level now, you will see it has risen. Now from the volume of the water displaced, calculate the weight of water from the following equation for density : Mass of water (in gm) Density of water is 1 gm/cm^{3}. You will see that the mass of water displaced is exactly equal to the reduction in weight of the stone in water.Density of water = Volume of water (in cubic cm) 
Archimedes was the first person to understand this phenomenon more than about 2,200 years ago and hence the phenomenon is named after him. Click here for an interesting anecdote on Archimedes.
Archimedes’ Principle states that a body immersed in a liquid, wholly or partly, loses its weight. The loss of weight is equal to the weight of the liquid displaced by the body.
2. Theoretical proof of Archimedes’ Principle
Consider the figure alongside, here a square piece of iron is immersed in liquid. The piece of iron is experiencing forces from all sides and they are:

Since the piece of iron is stationary and is not moving either up or down or side ways, we can safely say that
H=0 and
H=0 and
Total upward force = Total Downward force
T+ F_{2} = W + F_{1 }
Pressure is defined as force per unit area.
F_{1} = P_{1} (on the upper surface of the iron piece) x area
and
F_{2} = P_{2} (on the lower surface of the iron piece ) x area.
Pressure at a point inside a liquid is proportional to the height at which the point is from the surface, multiplied by the density of the liquid () and the gravitational force. In the above figure the pressure at the top surface of the iron piece is h_{1} g and at the bottom surface is h_{2} g.
Therefore F_{1} = (h_{1} g) x area and F_{2} = (h_{2} g) x area
W  T = ( g ) x volume of the iron piece
W  T = loss of the weight of the iron piece when immersed in liquid.
( g ) x volume of the iron piece = ( g) x volume of the liquid displaced by the iron piece
= g x V = (mass of liquid displaced) x g
= weight of liquid displaced by the body
Hence we can conclude that the loss of weight of a body in a liquid is equal to the weight of the liquid displace by the body.
The Archimedes principle holds good for irregular as well as regular bodies and any liquids.
3. Application of Archimedes’ Principle to determine densities of liquids
Density of substance Density of water Density of water is 1 gm/cm^{3}. (Density changes with temperature; density of water is 1 gm/cm^{3} at 4^{o}C. It is taken as the same at all temperatures unless the temperatures are close to 0^{o}C or 100^{o}C , where water changes to ice or steam respectively) To determine the density of an unknown liquid by Archimedes’ method, please do the following :

Weight of the displaced liquid Volume of water displaced
R. D = X
Volume of the displaced liquid Weight of the water displaced
R. D = X
Volume of the displaced liquid Weight of the water displaced
Since the volume displaced by the object in both liquid and water is same, they get cancelled out from the above equation.
(W_{1}  W_{3 })
R.D. =
(W_{1}  W_{2 })
(W_{1}  W_{2 })
Summary
In this chapter we have seen what Archimedes’ Principle is. The principle has wide applications in our everyday lives. We have also seen how relative densities of liquids can be determined from Archimedes’ Principle.
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