The value of Young.s modulus of elasticity for a perfectly rigid body is :

Options

A. Zero
B. Infinite
C. 1
D. 100

Answer

To solve the question regarding the value of Young's modulus of elasticity for a perfectly rigid body, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (E) is defined as the ratio of stress (σ) to strain (ε). Mathematically, it is expressed as:
\[ E = \frac{\sigma}{\epsilon} \]

2. **Defining Stress and Strain**:
- **Stress (σ)** is defined as the force (F) applied per unit area (A):
\[ \sigma = \frac{F}{A} \]
- **Strain (ε)** is defined as the change in length (ΔL) divided by the original length (L₀):
\[ \epsilon = \frac{\Delta L}{L_0} \]

3. **Considering a Perfectly Rigid Body**:
A perfectly rigid body is one that does not deform under any applied stress. This means that no matter how much force is applied, the length of the body does not change.

4. **Calculating Strain for a Perfectly Rigid Body**:
Since there is no change in length for a perfectly rigid body, the change in length (ΔL) is zero:
\[ \Delta L = 0 \implies \epsilon = \frac{0}{L_0} = 0 \]

5. **Substituting into Young's Modulus Formula**:
Now, substituting the values of stress and strain into the Young's modulus formula:
\[ E = \frac{\sigma}{\epsilon} = \frac{\sigma}{0} \]
Since division by zero is undefined in mathematics, we can interpret this scenario as Young's modulus tending towards infinity.

6. **Conclusion**:
Therefore, the value of Young's modulus of elasticity for a perfectly rigid body is:
\[ E = \infty \]

### Final Answer:
The value of Young's modulus of elasticity for a perfectly rigid body is infinity.