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Fundamentals Of Physics
Found in: Page 409

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Short Answer

An iron casting containing a number of cavities weighs 6000 N in air and 4000 N in water. What is the total volume of all the cavities in the casting? The density of iron (that is, a sample with no cavities) is 7.87 g/cm3.

The total cavity volume in the casting is 0.126 m3

See the step by step solution

Step by Step Solution

Step 1: The given data

  • The weight of iron casting in air, W=6000 N
  • The weight of iron casting in water, Weff=4000 N
  • The density of solid iron, ρiron=7.87gcm3 or 7.87×103 kgm3

Step 2: Understanding the concept of Archimedes Principle

We can use the concept of Archimedes’ principle and expression of density. When an iron casting is fully submerged in water, then a buoyant force from the surrounding fluid acts on it. This force has a magnitude equal to the weight of the water displaced by the iron casting.


Force applied on body (or weight), Fb=mfg (i)

Density of a substance, ρ=mV (ii)

Step 3: Calculation of total volume of cavity

The volume of cavity is the difference between volume of casting and volume of iron. Hence,

Vcavity=Vcasting=Viron (iii)

According to equation (ii), we get

The volume of iron as:

Viron=mironρiron =gmirongρiron =Wgρiron

When the iron casting is submerged in water, the forces acting on it are Fg-Fb. Hence,the effective weight in water is given as:


Equation (iii) becomes and using the given values, we get

Vcavity=W-Weffgρw-Wgρiron =6000 N-4000 N9.8ms2×1000kgm3-6000 N9.8ms2×7.87×103kgm3 =0.126 m3

Hence, the volume of cavity is 0.126 m3

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