Question

Modulus of rigidity is defined as the ratio of:
A. Longitudinal stress to longitudinal strain
B. Volumetric Stress to Volumetric Strain
C. Shear Stress to Shear Strain
D. Linear Stress to Linear Strain

Answer 1

Hint: Rigidity is a property of a body due to which the body cannot bend or change its shape. The modulus of rigidity is the measure of the rigidity of a body. This property depends on the elasticity of the material and the amount of force it can handle.


Complete step by step answer:
Modulus of rigidity is also known as shear modulus on a material. It is one of the most important mechanical properties of solids. The modulus of rigidity gives as the ratio is mathematically given by the ratio of the shearing stress and strain of a body. It is denoted by $G$.
$G=\dfrac{\text{shear stress}}{\text{shear strain}}$
The SI unit of Modulus of rigidity is pascal (Pa).
Dimension: $[{{M}^{1}}{{L}^{-1}}{{T}^{-2}}]$
Shearing Stress is the ratio of the force applied on the body to the area on which the force is applied.
$shear\,stress=\dfrac{F}{A}$
Shearing strain is the ratio of the transverse displacement of the surface of the body to the initial length of the body.
$shear\,stain=\dfrac{\Delta x}{l}$
The rigidity of material represents its ability to resist the external forces and be in its original state.

So, the correct answer is “Option C”.

Note: Commonly the modulus of rigidity is expressed in the terms of Giga Pascal (GPa). It can even be expressed in the form of pounds per square inch (PSI). It is also known as one of the elastic coefficients of material. Some other elastic coefficients of a material are Young’s Modulus, Bulk Modulus of the body.