Question

For a material, the modulus of Rigidity is 100 GPa and Poisson's ratio is 0.25. The
value of elastic modulus in GPa is​

Answer 1

Given:

The modulus of Rigidity = 100 GPa

Poisson's ratio = 0·25

To Find:

We have to find the elastic modulus of the material in GPa.

Solution:

The relationship between Elastic modulus and  shear modulus is given by,

                    $\[E = 2G\left( {1 + \mu } \right)\]$

where

E is the Elastic modulus / Young's modulus

G is the Shear modulus / Modulus of rigidity

μ is the Poisson's ratio

By substituting the values of modulus of rigidity and Poisson's ratio, we get the value of elastic modulus.

∵         $\[\begin{array}{l}E = 2G\left( {1 + \mu } \right)\\\\E = 2 \times 100\left( {1 + 0 \cdot 25} \right)\\\\\,\,\,\,\, = 250\,GPa\end{array}\]$

∴ The value of elastic modulus is 250 GPa