Question

If the Poisson's ratio of the material is 0.25, then the ratio of modulus of rigidity to modulus of elasticity is

• A. 0.25
• B. 0.40
• C. 2.0
• D. 2.5

Hint:

Memorize the key relationships between elastic constants ($E$, $G$, $K$, $\nu$):
1. $E = 2G(1 + \nu)$
2. $E = 3K(1 - 2\nu)$
These two formulas are essential for solving many problems in strength of materials.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem asks us to determine the ratio of the modulus of rigidity to the modulus of elasticity when the Poisson's ratio of the material is known.

Step 2: Key Formula or Approach:
The elastic constants are related by the equation \(E=2G(1+\nu)\). Rearranging this expression gives the required ratio \(G/E\).

Step 3: Detailed Explanation:
The given value of Poisson's ratio is 0.25. Using the relation \(G/E=\frac{1}{2(1+\nu)}\), substitute \(\nu=0.25\). This gives \(G/E=\frac{1}{2(1.25)}=\frac{1}{2.5}=0.40\). Thus, the modulus of rigidity is 40% of the modulus of elasticity for the given material.

Step 4: Final Answer:
The ratio of modulus of rigidity to modulus of elasticity is 0.40.