For most materials the Youngs modulus is n times the modulus of rigidity, where n is

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To solve the question regarding the relationship between Young's modulus and the modulus of rigidity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Young's Modulus (E)**: It measures the tensile stiffness of a solid material and is defined as the ratio of tensile stress to tensile strain.
- **Modulus of Rigidity (G)**: Also known as shear modulus, it measures the material's response to shear stress and is defined as the ratio of shear stress to shear strain.

2. **Establish the Relationship**:
- For most materials, it is known that the modulus of rigidity (G) is related to Young's modulus (E) by the equation:
\[ G = \frac{E}{3} \]

3. **Rearranging the Equation**:
- From the above relationship, we can express Young's modulus in terms of the modulus of rigidity:
\[ E = 3G \]

4. **Identify the Value of n**:
- From the equation \( E = nG \), we can see that \( n \) is the factor by which Young's modulus is greater than the modulus of rigidity.
- Comparing this with our rearranged equation \( E = 3G \), we find that:
\[ n = 3 \]

5. **Conclusion**:
- Therefore, for most materials, the Young's modulus is \( n \) times the modulus of rigidity, where \( n = 3 \).

### Final Answer:
For most materials, the Young's modulus is 3 times the modulus of rigidity.

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