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 question asks for the ratio of the Modulus of Rigidity ($G$) to the Modulus of Elasticity ($E$), given the Poisson's ratio ($\nu$).

Step 2: Key Formula or Approach:
For an isotropic elastic material, the three main elastic constants are related by the following formula:
\[ E = 2G(1 + \nu) \] where:
$E$ = Modulus of Elasticity (Young's Modulus)
$G$ = Modulus of Rigidity (Shear Modulus)
$\nu$ = Poisson's ratio

Step 3: Detailed Explanation:
We are given the Poisson's ratio, $\nu = 0.25$.
We need to find the ratio $G/E$. We can rearrange the formula to solve for this ratio.
\[ \frac{E}{G} = 2(1 + \nu) \] Taking the reciprocal of both sides:
\[ \frac{G}{E} = \frac{1}{2(1 + \nu)} \] Now, substitute the given value of $\nu$:
\[ \frac{G}{E} = \frac{1}{2(1 + 0.25)} \] \[ \frac{G}{E} = \frac{1}{2(1.25)} \] \[ \frac{G}{E} = \frac{1}{2.5} \] \[ \frac{G}{E} = 0.40 \]

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