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
$\frac{9}{Y}=\frac{1}{K}+\frac{3}{\eta}$