Archimedes principle is about the upward thrust in the fluid to the object. It states that the upward thrust by the fluid applied on the object is equal to the weight of the displaced water by the object.
So that the weight of the water displaced by an object is less than the weight of the object, it will sink in the fluid. This is the reason, how large ship can float but a small needle does not float in the water.
Fb = ρgv
And Fb = Wa – Wf
ρgv = Wa – Wf
Fb = buoyant force
ρ = density of fluid
g = gravitational acceleration
v = volume of object
Wa = Weight of object in air
Wf = Weight of object in fluid.
Example: A balloon having a volume of 4.000 L is placed on a sensitive balance which registers a weight of 1.867 g. What is the "true weight" of the balloon if the density of the air is 1.294 g L^–1?
Solution: Applying archimedes principle,
Weight of the air displaced by the balloon = Volume x density
= 4 x 1.294 = 5.176 g
Therefore, The true weight = 1.867 + 5.176 = 7.043 gm
Example: The volume of 80 gm of substance is 30 cm^3. If the density of water if 1 gm/cm^3 . Will the substance float or sink?
Solution: We have given,
mass of substance = 80 gm
Volume of substance = 30 cm^3
So that, we can calculate the density of the substance.
Density = mass/volume = 80/30 = 2.67 gm/cm^3
As the density of substance is more than the density of water, therefore it will sink into the water.