Young’s modulus is defined as the ratio

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ISRO URSC Technical Assistant Mechanical 24 March 2019 Official Paper
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  1. volumetric stress and volumetric strain
  2. lateral stress and lateral strain
  3. longitudinal stress and longitudinal strain
  4. shear stress to shear strain

Answer (Detailed Solution Below)

Option 3 : longitudinal stress and longitudinal strain
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Explanation:

Young's Modulus (E): It is defined as the ratio of normal or longitudinal stress to longitudinal strain within the limit of proportionality.

\(E = \frac{{longitudinal\;stress}}{{longitudinal\;\;strain}} =\frac{σ}{ϵ}= \frac{{\frac{F}{A}}}{{\frac{{{\rm{Δ }}l}}{l}}} = \frac{{Fl}}{{A{\rm{Δ }}l}} \)

where σ = normal or longitudinal stress, ϵ = longitudinal strain, F = force applied, A = cross-section area normal to force, l = length, Δl = change in length,

Additional Information

 Bulk Modulus (K): 

  • When a solid or fluid (liquid or gas) is subjected to a uniform pressure all over the surface, such that the shape remains the same, then there is a change in volume.
  • Then the ratio of normal stress to the volumetric strain within the elastic limits is called the Bulk modulus. This is denoted by K.

\(K = \frac{{Normal\;stress}}{{volumetric\;strain}} = \frac{{\frac{F}{A}}}{{\frac{{ - {\rm{\Delta }}V}}{V}}} = - \frac{{pV}}{{{\rm{\Delta }}V}}\)

We know that, p = F/A

where p = increase in pressure; V = original volume; ΔV = change in volume

Modulus of Rigidity (G): Within limits of proportionality, the ratio of tangential stress to the shearing strain is called the modulus of rigidity of the material of the body and is denoted by η.

\(G = \frac{{Shearing\;stress}}{{Shearing\;strain}}\)

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