Question

The ratio of modulus of rigidity to bulk modulus for a Poisson's ratio of $0.25$ would be

• A. $2/3$
• B. $2/5$
• C. $3/5$
• D. $1.0$

Answer 1

The correct option is C $3/5$

$\text{Step 1: Relation betweeen Elastic Constant}$

Elastic constants are related by the following equation

$Y=2\eta (1+\sigma )$ $....\left(1\right)$

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

$\text{Step 2: Calculations}$

From equation $1$ and $2$, we get:

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

Putting value of $\sigma$ as $0.25$, we get:

$(1+0.25)2\eta =3K(1-0.5)$

$\Rightarrow$ $\frac{\eta }{K}=\frac{3}{5}$

Hence option $C$ is correct.