Question

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

• A. $0.5$
• B. $0.4$
• C. $0.3$
• D. $1.0$

Answer 1

The correct option is B $0.4$

$\text{Step 1: Relation between elastic constants}$

Using the relation between Youngs modulus $Y$, Rigidity modulus $\eta$ and Poisson ratio $\sigma$:

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

$\text{Step 2: Calculations}$

From equation $\left(1\right)$

$\frac{\eta }{Y}=\frac{1}{2(1+\sigma )}$

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

$\frac{\eta }{Y}=\frac{1}{2.5}=0.4$

Hence option $B$ is correct.