Question

Young's modulus of a metal is $15\times 10$${}^{11}$ Pa. If its poisson's ratio is $0.4$. The bulk modulus of the metal in $Pa$ is :

• A. $25\times 10$${}^{11}$
• B. $2.5\times 10$${}^{11}$
• C. $250\times 10$${}^{11}$
• D. $0.25\times 10$${}^{11}$

Answer 1

The correct option is A $25\times 10$${}^{11}$

Young's modulus $Y=15\times {10}^{11}$ (given)
Poisson's ratio $\sigma =0.4$
Using $\frac{Y}{3k}=1-2\sigma$ (standard result)
where $k$ is Bulk's modulus
Thus we get $Y=3k(1-2\sigma )$
$\therefore$ $15\times {10}^{11}=3(1-0.8)k$
$⟹k=25\times {10}^{11}$ $Pa$