Archimedes' Principle

Archimedes' Principle

Archimedes principle is the consequence of Pascal’s law. According to legend, Archimedes devised the principle of the “hydrostatic balance” after he noticed his own apparent loss in weight while sitting in his bath. The story goes that he was so enthused with his discovery that he jumped out of his bath and ran through the town, shouting "eureka". Archimedes principle states that ‘a body immersed in a fluid experiences a vertical upward buoyant force equal to the weight of the fluid it displaces’.

When a body is partially or completely immersed in a fluid at rest, it experiences an upthrust which is equal to the weight of the fluid displaced by it. Due to the upthrust acting on the body, it apparently loses a part of its weight and the apparent loss of weight is equal to the upthrust.

Thus, for a body either partially or completely immersed in a fluid,

Upthrust = Weight of the fluid displaced = Apparent loss of weight of the body.

Apparent weight of an object = True weight of an object in air – Upthrust (weight of water displaced)

Example 1.11

What is the mass of the object floating in the given diagram?

Solution:

Weight of the object = Buoyant force

ρ = 1000 kg m^-3

V = (25x10x10) cm³ = 2500 x 10^-6 m³

m = ρV = 1000 x 2500 x 10^-6 = 2.5 kg