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Liquids of different densities

That point through which the force of buoyancy acts is the center of buoyancy. This point lies at the center of gravity of the displaced liquid. The buoyant force of all the displaced liquid might be replaced by a single force acting through the center of buoyancy without alter­ing the behavior of the body.

Figure 28 - Test of Archime­des’ principle

Suspend from one arm of a balance (Figure 28) a hollow cylindrical cup and a piece of brass which has been nicely turned in the form of a cylinder so that it will just fit the cavity inside the cup. Now counterbalance the weight of the cup and cylinder by adding the necessary weights to another pan of the balance. When a vessel of water is brought up in such a way that the cylinder С is com­pletely immersed, it is observed that the side of the balance carrying the cylin­der rises, showing that the water is pushing up on the cylinder. If water is now poured into the cup until it is just filled, the equilibrium of the balance is restored. Since the weight of a volume of water equal to that displaced by the cylin­der is sufficient to compensate for the lifting effect of the water on the cylinder, it is evident that the cylinder is lifted up by a force equal to the weight of the displaced water. If the experiment is repeated with kerosene or some other liquid instead of water, the same result will always be obtained. The loss in the weight of the immersed body is equal to the weight of the volume of liquid displaced by it.

This analysis and the preceding experiment makes it possible to formulate Archimedes’ principle which states that the loss of weight of a body immersed in a fluid is equal to the weight of the dis­placed fluid, or a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by it.

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