Young's modulus of a perfectly rigid body is

Options

A. zero
B. unity
C. finite and low
D. infinite

Answer

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

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (Y) is defined as the ratio of stress (force per unit area) to strain (deformation per unit length) in a material. It is given by the formula:
\[ Y = \frac{\text{Stress}}{\text{Strain}} \]

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

3. **Characteristics of a Perfectly Rigid Body**:
A perfectly rigid body is one that does not deform under any applied load. This means that:
- The change in length (ΔL) is zero when a force is applied.
- Therefore, the strain (ΔL/L) is also zero.

4. **Calculating Young's Modulus for a Perfectly Rigid Body**:
Since strain is zero for a perfectly rigid body, we can substitute this into the Young's modulus formula:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\frac{F}{A}}{0} \]
This results in a division by zero, which mathematically leads to:
\[ Y = \infty \]

5. **Conclusion**:
Hence, the Young's modulus of a perfectly rigid body is considered to be infinite.

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

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