Question

The Young's modulus of a material is ${10}^{11}N{m}^{-2}$ and its poisson's ratio is 0.2. The modulus of rigidity of the meterial is

• A. $0.42\times {10}^{11}N{m}^{-2}$
• B. $0.42\times {10}^{14}N{m}^{-2}$
• C. $0.42\times {10}^{16}N{m}^{-2}$
• D. $0.42\times {10}^{18}N{m}^{-2}$

Answer 1

The correct option is A $0.42\times {10}^{11}N{m}^{-2}$

$\text{Relation btw youngs modulus, Rigidity modulus and}$

$\text{Poissons ratio}is:$

$y=2\eta (1+\sigma )$

$\text{Here}\eta \text{is Rigidity modulus.}$

$\begin{array}{cc}\text{Given:}\sigma & =0.2\text{and}Y={10}^{11}\\ {10}^{11}& =2\eta \left(1.2\right)\\ \eta & ={10}^{11}\times \frac{1}{2.4}\\ \eta & =0.42\times {10}^{11}{Nm}^{-2}\end{array}$