Question

The relationship between Young’s modulus (E), Bulk modulus (K) and Poisson’s ratio ($\mu$) is given by

• A. $E = 2K(1-2\mu)$
• B. $E = 3K(1-2\mu)$
• C. $E = 3K(1-3\mu)$
• D. $E = 2K(1-3\mu)$

Hint:

Remember the three important elastic relations: $E = 2G(1+\mu)$, $E = 3K(1-2\mu)$, and $K = \dfrac{E}{3(1-2\mu)}$.

Answer 1

The Correct Option is B

Step 1: Recall standard elastic relations.
In the theory of elasticity, Young’s modulus, bulk modulus, and Poisson’s ratio are interrelated material properties for isotropic and homogeneous materials.
Step 2: Write the known relation.
The standard formula connecting Young’s modulus ($E$), bulk modulus ($K$), and Poisson’s ratio ($\mu$) is given by:
\[ E = 3K(1 - 2\mu) \]
Step 3: Match with the options.
Comparing the derived relation with the given options, it directly matches option (B).
Step 4: Conclusion.
Hence, the correct relationship is $E = 3K(1 - 2\mu)$.