Class 11 Physics Mechanical Properties of Solids Volume Strain

Volume Strain

  • Volume strain is defined as ratio of change in volume to the original volume as a result of the hydraulic stress.
  • When the stress is applied by a fluid on a body there is change in the volume of body without changing the shape of the body. 
  • Volume strain = ΔV/V 
  • For example:-
  • Consider a ball initially at volume V.

 

  • Because of hydraulic stress there is change in volume V’ 

  • Therefore, Change in the volume ΔV= V’ – V 
  • Conclusion: - Deformation is measured using strain. 
  • Consider a cube whose initial volume is V. 
  • When the cube is subjected to stress there will be a change in the volume but the shape will not change.

 

Problem:- Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 cm and compressional strain of each column.

Answer:

Mass of the big structure, M = 50,000 kg 

Inner radius of the column, r = 30 cm = 0.3 m

Outer radius of the column, R = 60 cm = 0.6 m

Young’s modulus of steel, Y = 2 × 1011 Pa

Total force exerted, F = Mg = 50000 × 9.8 N

Stress = Force exerted on a single column = 122500 N

Young’s modulus, Y =𝑆𝑡𝑟𝑒𝑠𝑠/𝑆𝑡𝑟𝑎𝑖𝑛

Where,

Area, A = π (R2 – r2) = π ((0.6)2 – (0.3)2)

Strain = 122500/ (π [0.6)2 – (0.3)2] x 2x1011)

= 7.22 × 10–7

Hence, the compressional strain of each column is 7.22 × 10–7

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