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

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