Question

15. Derive the relation for modulus of rigidity
it's for 2 marks​

Answer 1

Answer:Rigidity modulus of any elastic solid are together called as Elastic constants. When a deforming force is acting on a solid. It results in the change in its original dimension. In such cases, we can use the relation between elastic constants to understand the magnitude of deformation.(thi s can be the intro)

Young modulus can be expressed using Bulk modulus and Poisson’s ratio as –

E=3K(1−2μ)

Similarly, Young’s modulus can also be expressed using rigidity modulus and Poisson’s ratio as-E=2G(1+2μ)

Combining the above two equation and solving them to eliminate Poisson’s ratio we can get relation between Young’s modulus and bulk modulus k and modulus of rigidity as -E=9KGG+3K