Question

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

• A. \( \frac{2}{3} \)
• B. \( \frac{2}{5} \)
• C. \( \frac{3}{5} \)
• D. \( 1 \)

Hint:

Understanding the relationships between different elastic constants is crucial for material selection and mechanical design.

Answer 1

The Correct Option is A

Using the relationship between Young's modulus (E), modulus of rigidity (G), and bulk modulus (K) with Poisson's ratio (\(\nu\)): \[ G = \frac{E}{2(1+\nu)} \quad \text{and} \quad K = \frac{E}{3(1-2\nu)} \] For \(\nu = 0.25\), the ratio \( \frac{G}{K} \) becomes: \[ \frac{G}{K} = \frac{\frac{E}{2(1+0.25)}}{\frac{E}{3(1-2 \times 0.25)}} = \frac{3}{2} \times \frac{1.5}{2} = \frac{9}{12} = \frac{3}{4} \]