Question

The relation between $Y,K$ and $\eta$ is

• A. $\frac{3}{Y}=\frac{1}{3K}+\frac{1}{\eta }$
• B. $\frac{1}{Y}=\frac{1}{9K}+\frac{1}{\eta }$
• C. $\frac{9}{Y}=\frac{1}{K}+\frac{3}{\eta }$
• D. $\frac{1}{\eta }=\frac{1}{K}+\frac{1}{Y}$

Answer 1

The correct option is A $\frac{3}{Y}=\frac{1}{3K}+\frac{1}{\eta }$

$\text{The Relalion between Young's modulus}Y\text{, Bulk modulus k, modulus of elastiaty is}\eta \text{. We know}\to$

$\begin{array}{c}Y=3K(1-2)\sigma \to \text{(1)}(\sigma =\text{stress})\\ Y=2\eta (1+\sigma )⟶\text{(2)}\end{array}$

$\begin{array}{c}\text{using (1)}\&\left(2\right)\text{, eliminating}\sigma \\ \Rightarrow \frac{3}{Y}=\frac{1}{\eta }+\frac{1}{3k}\\ \end{array}$