Question

If the ratio of Young's modulus to bulk modulus of a material is \( \frac{3}{2} \), then the ratio of shear modulus to the Young's modulus of the material is

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

Hint:

The relationship between the moduli is critical for understanding material deformation under various loading conditions. The ratio of Young's modulus to bulk modulus gives insight into the shear modulus.

Answer 1

The Correct Option is B

The relationship between Young's modulus \( E \), bulk modulus \( K \), and shear modulus \( G \) is given by the following equation: \[ \frac{E}{K} = \frac{3}{2} \text{and} \frac{E}{G} = 2 \left( \frac{1 + \mu}{3(1 - 2\mu)} \right) \] From the given information, we find that the ratio of shear modulus to Young's modulus is \( \frac{2}{5} \). The correct answer is (B).
Final Answer: (B) \( \frac{2}{5} \)