Question

The relation between Young's modulus $Y$, bulk modulus $K$ and modulus of elasticity $\sigma$ is

• A. $\frac{1}{y}=\frac{1}{k}+\frac{3}{\eta }$
• B. $\frac{3}{y}=\frac{1}{\eta }+\frac{1}{3k}$
• C. $\frac{1}{y}=\frac{3}{\eta }+\frac{1}{3k}$
• D. $\frac{1}{\eta }=\frac{3}{y}+\frac{1}{3k}$

Answer 1

The correct option is B $\frac{3}{y}=\frac{1}{\eta }+\frac{1}{3k}$

We know that,

$Y=3K(1-2\sigma )$

or, $\sigma =\frac{1}{2}(1-\frac{Y}{2K})$ ----------(i)

Also, $Y=2\eta (1+\sigma )$

or, $\sigma =\frac{Y}{2\eta }-1$ ----------(ii)

Now, From (i) and (ii),

$\frac{1}{2}(1-\frac{Y}{3K})=\frac{Y}{2\eta }-1$

or, $1-\frac{Y}{3K}=\frac{Y}{\eta }-2$

or, $\frac{3}{Y}=\frac{1}{\eta }+\frac{1}{3K}$