As an example, a 3.80 - kg aluminum ball has an apparent mass of 2.00 kg when submerged in a particular liquid: calculate the density of the liquid.

The density of the liquid = 1278.95 kg/m³

Explanation:

Density: This can be defined as the ratio of the mass of a body to its volume. The S. I unit of density is kg/m³.

From Archimedes principle,

R. d = Density of object/Density of liquid = Weight of object in air/Upthrust in liquid.

D₁/D₂ = W/U ... Equation 1

D₂ = D₁ (U/W) ... Equation 2

Where D₁ = Density of aluminum, D₂ = Density of liquid, W = weight of aluminum, U = upthrust.

m₁ = 3.8 kg, m₂ = 2.00 kg, g = 9.8 m/s²

W = m₁g = 3.8 (9.8) = 37.24 N.

U = lost in weight of the aluminum = (m₁ - m₂) g = (3.8-2.0) 9.8

U = 1.8 (9.8) = 17.64 N.

Constant: D₁ = 2700 kg/m³

Substituting these values into equation 2

D₂ = 2700 (17.64) / 37.24

D₂ = 1278.95 kg/m³

Thus the density of the liquid = 1278.95 kg/m³