For most of the material , Young's modulus (Y) and rigidity modulus (G) are related as

Options

A. G=3Y
B. `G=(Y)/(3)`
C. `G=(3)/(2)Y`
D. `G=(Y)/(8)`

Explanation

To solve the question regarding the relationship between Young's modulus (Y) and rigidity modulus (G) for most materials, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Young's Modulus (Y) is a measure of the stiffness of a solid material and is defined as the ratio of tensile stress to tensile strain.
- Rigidity Modulus (G), also known as shear modulus, is the ratio of shear stress to shear strain.

2. **Know the Relationship**:
- For isotropic materials (materials that have identical properties in all directions), there is a known relationship between Young's modulus (Y), rigidity modulus (G), and Poisson's ratio (σ):
\[ Y = 2G(1 + \sigma) \]

3. **Rearranging the Equation**:
- We can rearrange the equation to express G in terms of Y and σ:
\[ G = \frac{Y}{2(1 + \sigma)} \]

4. **Approximation for Most Metals**:
- For many metallic materials, the Poisson's ratio (σ) typically ranges from 0.25 to 0.35. If we take an average value of σ ≈ 0.3, we can approximate:
\[ G \approx \frac{Y}{2(1 + 0.3)} = \frac{Y}{2 \times 1.3} \approx \frac{Y}{2.6} \]
- This can further be approximated to:
\[ G \approx \frac{Y}{3} \]

5. **Conclusion**:
- Therefore, for most metallic materials, we can say that:
\[ Y \approx 3G \]
- This implies that Young's modulus is approximately three times the rigidity modulus for most materials.

### Final Answer:
For most materials, Young's modulus (Y) and rigidity modulus (G) are related as:
\[ Y \approx 3G \]