Archimedes Principle equation

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Archimedes principle says that the weight of the displaced water because of an object in the fluid is equal to the buoyant force acting on it. We can also say that an object can displace the equal weight of water by its own weight.
Equation:
                             Fb = ρgv

Where, Fb = buoyant force

          ρ = density of the fluid

          g = gravitational acceleration

          v = volume of object
 
We can also write,

                             Fb = Wa – Wf

Where, Wa = weight of object in air

          Wf = weight of object in fluid

So that we have the equation,

                   ρgv = Wa – Wf

 
Example: An object weighs 50 g in air and has a volume of 24.0 cm^3. What will be its apparent weight when immersed in water?

Solution: According to the archimedes principle, When the object is immersed in water, it displaces same amount of water.
          We have given, volume of object = 24 cm^3
          Consider density of water as unity.
So, mass = volume x density
           = 24 x 1 = 24 g
Therefore, Apparent weight = 50 – 24 = 26 gm.
 

Example: The volume of a 400 gm sealed packet is 250 cm^3. Will the packet float or sink in water if the density of water is 1 gm/cm^3. What will be the mass of water displaced by this packet?

Solution: Given that,
          Mass of substance = 400 gm
          Volume of substance = 250 cm^3
So, density = mass/volume = 400/250 = 1.6 gm/cm^3
As the density of substance is more than the density of water. therefore it will sink in the water.
Mass of water displaced by the packet = volume x density
                             = 250 x 1 = 250 gm.
 
 

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