Question

The elastic constants, modulus of rigidity ‘K’ and modulus of elasticity ‘E’ are related through Poisson’s ratio ‘$\mu$’ as:

• A. \( \frac{E}{3(1 - 2\mu)} \)
• B. \( E(1 - 2\mu) \)
• C. \( 3E(1 - 2\mu) \)
• D. \( \frac{E}{3(1 + 2\mu)} \)

Hint:

Remember: \( K = \frac{E}{3(1 - 2\mu)} \) and \( G = \frac{E}{2(1 + \mu)} \) — useful for solving many elasticity problems.

Answer 1

The Correct Option is A

The relationship between elastic constants — modulus of elasticity (E), bulk modulus (K), and Poisson’s ratio (\( \mu \)) — is given by the following formula: \[ K = \frac{E}{3(1 - 2\mu)} \] Where: 
- \( K \) = bulk modulus (not modulus of rigidity — a minor error in the image wording), 
- \( E \) = modulus of elasticity, 
- \( \mu \) = Poisson’s ratio.
This formula helps relate how a material compresses volumetrically under pressure.
Other elastic relations include: 
- \( G = \frac{E}{2(1 + \mu)} \), where \( G \) is the modulus of rigidity or shear modulus.