Question

The different relations for Young's Modulus (E), Bulk Modulus (K) and Modulus of Rigidity (G) are given by:
A. \(E = 2G(1 + \mu)\), \(\mu\) is Poisson's ratio
B. \(E = 3K(1 + 2\mu)\)
C. \(E = 2G(1 - \mu)\)
D. \(E = 3K(1 - 2\mu)\)
E. \(E = 2K(1 - 2\mu)\)
Choose the most appropriate answer from the options given below:

• (A) and (B) only
• (C) and (D) only
• (A) and (D) only
• (C) and (E) only

Hint:

Elastic relations:
E = 2G(1 + \(\mu\)), E = 3K(1 - 2\(\mu\)).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Elastic constants are related to each other.
The relationships involve Poisson's ratio.

Step 2: Key Formula or Approach:
\(E = 2G(1 + \mu)\) and \(E = 3K(1 - 2\mu)\).

Step 3: Detailed Explanation:
A. \(E = 2G(1 + \mu)\) - correct.
B. \(E = 3K(1 + 2\mu)\) - incorrect.
C. \(E = 2G(1 - \mu)\) - incorrect.
D. \(E = 3K(1 - 2\mu)\) - correct.
E. \(E = 2K(1 - 2\mu)\) - incorrect.
Thus, A and D are correct.

Step 4: Final Answer:
The correct relations are (A) and (D).
Hence, the correct option is (C).