For a given material, Young's modulus is 2.4 times that of rigidity modulus. Its Poisson's ratio is

Options

A. 2.4
B. 1.2
C. 0.4
D. 0.2

Explanation

To find the Poisson's ratio given that Young's modulus (Y) is 2.4 times the rigidity modulus (η), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Young's modulus, rigidity modulus, and Poisson's ratio**:
The relationship is given by the formula:
\[ Y = 2η(1 + σ) \]
where:
- \( Y \) = Young's modulus
- \( η \) = Rigidity modulus
- \( σ \) = Poisson's ratio

2. **Substitute the given relationship into the formula**:
We know from the problem that:
\[ Y = 2.4η \]
Now, we can substitute this into the formula:
\[ 2.4η = 2η(1 + σ) \]

3. **Simplify the equation**:
Divide both sides of the equation by \( η \) (assuming \( η \neq 0 \)):
\[ 2.4 = 2(1 + σ) \]

4. **Solve for \( σ \)**:
Divide both sides by 2:
\[ 1.2 = 1 + σ \]
Now, subtract 1 from both sides:
\[ σ = 1.2 - 1 \]
\[ σ = 0.2 \]

5. **Conclusion**:
The Poisson's ratio \( σ \) is 0.2.

### Final Answer:
The Poisson's ratio is \( σ = 0.2 \).