Young's Modulus And Elastic Modulus

Young’s Modulus (also referred to as the Elastic Modulus or Tensile Modulus), is a measure of mechanical properties of linear elastic solids like rods, wires and such. There are other numbers which give us a measure of elastic properties of a material, like Bulk modulus and shear modulus, but the value of Young’s Modulus is most commonly used. This is because it gives us information about the tensile elasticity of a material (ability to deform along an axis).

Young’s Modulus

The Young’s Modulus of such a material is given by the ratio of stress and strain, corresponding to the stress of material. The relation is given below.

\(E\) = \(\frac{\sigma}{\epsilon}\)


\(E\) is the Young’s Modulus of the material given in \(N/m^{2}\)
\(\sigma\) is the stress applied on the material
\(\epsilon\) is the strain corresponding to applied stress in the material

With the value of Young’s modulus for a material, the rigidity of the body can be determined. This is because it tell us about the body’s ability to resist deformation on application of force.

The Young’s Modulus values \((x 10^{9} N/m^{2})\) of different material are given below:

  • Steel – 200
  • Glass – 65
  • Wood – 13
  • Plastic (Polystyrene) – 3

Quite obviously we can claim that Steel is a lot more rigid in nature than wood or polystyrene, as in its tendency to experience deformation under applied load is less. Young’s modulus is also used to determine how much a material will deform under a certain applied load.

Another thing to keep in mind is that the lower the value of Young’s Modulus in materials, the more is the deformation experienced by the body and this deformation in case of objects like clay and wood can vary in the one sample itself. One part of the clay sample deforms more than the other whereas a steel bar will experience an equal deformation throughout.

Try calculating the change in length of a steel beam, whose initial length was 200m, due to an applied stress of \(1.5 N/m^{2}\). The Young’s modulus of steel can be found in the table above.

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Practise This Question

A copper wire of length 1.0 m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. If the Young's moduli of copper and steel are 1.0×1011 Nm2 and 2.0×1011 Nm2, the total extension of the composite wire is