Question

Poisson ratio for a material is 0.3 and its bulk modulus is $1.5\times {10}^{11}N/m^2$. Young's modulus of the material is-

• A. $2\times {10}^{11}N/m^2$
• B. $1.85\times {10}^{11}N/m^2$
• C. $1.8\times {10}^{11}N/m^2$
• D. $1.4\times {10}^{11}N/m^2$

Answer 1

Answer: (C)

$1.8\times {10}^{11}N/m^2$

$\begin{array}{c}\text{Given ithat}\\ \text{Bulk modulus}\left(\beta \right)=1.5\times {10}^{11}N/m^2\\ \text{Poisson ratio}\left(\sigma \right)=0.3\\ \text{Young modulus}\left(y\right)=?\\ \text{we know velation between}\beta ,\sigma ,y\end{array}$

$\beta =\frac{y}{3(1-2\sigma )}$

$y=3\beta (1-2\sigma )$

Putting value we get $$\begin{array}{cc}y& =3\times 1.5\times {10}^{11}(1-0.6)\\ y& =1.8\times {10}^{11}N/m^2\end{array}$$