An iron anchor of density 7810.00 kg/m^3 appears 252 N lighter in water than in air. (a) What is the volume of the anchor? (b) How much does it weigh in air?

(a) The volume of the iron anchor = 25.2 m³

(b) The mass of iron = 196812 kg

Explanation:

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

(a)

From Archimedes principle, the iron will displace a volume of water that is equal to its volume. And the weight of water displaced is equal to loss in weight or upthrust.

Therefore, Upthrust = lost in weight = weight of water displace.

Therefore, Volume of the iron = mass of water displace/density of water

Vi = m₁/D₁ ... Equation 1

Where Vi = volume of iron, m₁ = mass of water displaced, D₁ = Density of water.

Given: upthrust = 252 N, ∴ m₁ = 252/10 = 25.2 kg.

Constant: D₁ = 1.0 kg/m³

Substituting these values into equation 1,

Vi = 25.2/1.0

Vi = 25.2 m³

Therefore the volume of the iron anchor = 25.2 m³

(b)

Density of the iron = mass of the iron/volume of the iron.

Therefore, Mass of the iron = Density of the iron * volume of the iron ... equation 2

Given: Density of the iron = 7810 kg/m³, Volume of the iron = 25.2 m³

Substituting these values into equation 2,

Mass of the iron = 7810*25.2

Mass of the iron = 196812 kg.

Therefore the mass of iron = 196812 kg