Young's modulus of a perfectly rigid body is

Options

A. 1
B. 0
C. `oo`
D. Depends on condition

Explanation

To determine the Young's modulus of a perfectly rigid body, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Young's Modulus**:
Young's modulus (Y) is defined as the ratio of stress (force per unit area) to strain (relative change in length). The formula is given by:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\frac{F}{A}}{\frac{\Delta L}{L_0}} \]
where \( F \) is the applied force, \( A \) is the cross-sectional area, \( \Delta L \) is the change in length, and \( L_0 \) is the original length.

2. **Consider a Perfectly Rigid Body**:
A perfectly rigid body is one that does not deform under any applied force. This means that the change in length (\( \Delta L \)) is zero when a force is applied.

3. **Substitute into the Young's Modulus Formula**:
Since for a perfectly rigid body, \( \Delta L = 0 \), we can substitute this into the Young's modulus formula:
\[ Y = \frac{F/A}{\Delta L/L_0} = \frac{F/A}{0/L_0} \]

4. **Evaluate the Expression**:
The denominator becomes zero because \( \Delta L = 0 \). This leads to:
\[ Y = \frac{F/A}{0} = \infty \]
Thus, the Young's modulus of a perfectly rigid body tends to infinity.

5. **Conclusion**:
Therefore, the Young's modulus of a perfectly rigid body is infinite.

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

---