Question

There relation between $Y$ (Young's modulus), $K$ (bulk modulus) and $\eta$ (shear modulus) is

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

Answer 1

Answer: (A)

From small strain, the ratio of longitudinal stress to corresponding longitudinal strain is defined as the Young's modulus $(V)$ of the body.
In response to hydrostatic load, the specimen will change its volume, its resistance to do so $i_0$ quantified as bulk modulus $K$, whereas ratio of shear stress to the shear strain is defined as shear modulus $(\eta )$.
The relation between the three is given by
$\frac{9}{Y}=\frac{1}{K}+\frac{3}{\eta }$