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3 years ago

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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) Ho

w much does it weigh in air?

1 answer:

RSB [31]3 years ago

8 0

Answer:

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

<em>(b)The mass of iron = 196812 kg</em>

Explanation:

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

(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.

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

<em>Constant: D₁ = 1.0 kg/m³</em>

<em>Substituting these values into equation 1,</em>

Vi = 25.2/1.0

Vi = 25.2 m³

Therefore the volume of the iron anchor = 25.2 m³

(b)

<em>Density of the iron = mass of the iron/volume of the iron.</em>

<em>Therefore, Mass of the iron = Density of the iron × volume of the iron...........................................equation 2</em>

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

<em>Substituting these values into equation 2,</em>

<em>Mass of the iron = 7810×25.2</em>

<em>Mass of the iron = 196812 kg.</em>

<em>Therefore the mass of iron = 196812 kg</em>

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