A person who weighs 509,45 N empties her lungs as much as

possible and is then completely immersed in water (of density 1 000

kg/m3) while suspended from a harness. Her apparent weight is now

22,34 N. What is her density? Answer in two decimal places.

The weight of the girl = 1045.86 kg/m³

Explanation:

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

From Archimedes principle,

R. d = Density of the person/Density of water = Weight of the person in air/Upthrust.

⇒ D₁/D₂ = W/U ... Equation 1.

Where D₁ = Density of the person, D₂ = Density of water, W = Weight of the person in air, U = Upthrust in water.

Making D₁ the subject of the equation,

D₁ = D₂ (W/U) ... Equation 2

Given: D₂ = 1000 kg/m³, W = 509.45 N, U = lost in weight = weight in air - weight in water = 509.45 - 22.34 = 487.11 N

Substituting these values into equation 2

D₁ = 1000 (509.45/487.11)

D₁ = 1045.86 kg/m³

Thus the weight of the girl = 1045.86 kg/m³