Question

Which of the following is the correct order of magnitude of various elastic moduli in materials like aluminium and copper?
(A) Young’s moduli < Shear moduli < Bulk moduli
(B) Bulk moduli < Shear moduli < Young’s moduli
(C) Shear moduli < Young’s moduli < Bulk moduli
(D) Bulk modulus < Young’s moduli < Shear moduli

Answer 1

Hint: In the stress – strain curve, the region which is in elastic limit describes the maximum stress the material will take before deforming permanently. The ratio between stress and strain is the modulus of elasticity. Elastic moduli are of three types – Young’s modulus, Shear modulus and Bulk modulus.

Complete step by step solution:
From the stress – strain curve, the region which is in elastic limit describes the maximum stress the material will take before deforming permanently. This region is important to manufacturing and structural sectors.
The elastic modulus can be defined as the ratio between stress and strain.
There are three types of elastic moduli:
Young’s modulus – Young’s modulus can be defined as the mechanical property to withstand the compression and elongation with respect to its length. It is denoted by $Y$. It quantifies the relationship between stress and strain. It is the measure of mechanical properties of linear elastic solids.
Shear modulus – This modulus can be defined as the ratio between shear stress and shar strain. It can be denoted by $\eta $. The S.I unit of shear modulus is pascals but it is generally expressed in gigapascals.
Bulk modulus – It is used to measure the resistance property of the substance. It describes how resistant to compression the substance is. It is denoted by $K$.
Now, the magnitude of various elastic moduli of copper are –
$
  Y = 128 GPa \\
  K = 140GPa \\
  \eta = 48GPa \\
 $
Therefore, for copper, Shear moduli < Young’s moduli < Bulk moduli

Hence, the correct option is (C).

Note: The Young’s modulus can describe the ability of the body to resist deformation on the application of force, so by using the value of Young’s modulus of the material we can also determine the rigidity of the body.