For a perfectly rigid body

Options

A. Young's modulus is infinite and bulk modulus is zero.
B. Young's modulus is zero and bulk modulus is infinite.
C. Young's modulus is infinite and bulk modulus is also infinite.
D. Young's modulus is zero and bulk modulus is also zero.

Explanation

To solve the question regarding the properties of a perfectly rigid body, we need to analyze the definitions of Young's modulus and Bulk modulus and their implications for a rigid body.

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
- Young's modulus (E) is defined as the ratio of stress (force per unit area) to strain (deformation/original length).
- Mathematically, it is given by:
\[ E = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L_0} \]
- For a perfectly rigid body, when a force is applied, there is no deformation (strain = 0). Therefore, the strain approaches zero.

2. **Calculating Young's Modulus for a Rigid Body**:
- Since strain is zero, the formula for Young's modulus becomes:
\[ E = \frac{F/A}{0} \rightarrow \infty \]
- Hence, for a perfectly rigid body, Young's modulus is infinite.

3. **Understanding Bulk Modulus**:
- Bulk modulus (K) is defined as the ratio of change in pressure to the relative change in volume.
- Mathematically, it is given by:
\[ K = -V \frac{dP}{dV} \]
- For a perfectly rigid body, when pressure is applied, there is no change in volume (ΔV = 0).

4. **Calculating Bulk Modulus for a Rigid Body**:
- Since the change in volume is zero, the formula for Bulk modulus becomes:
\[ K = -V \frac{dP}{0} \rightarrow \infty \]
- Thus, for a perfectly rigid body, Bulk modulus is also infinite.

5. **Conclusion**:
- Both Young's modulus and Bulk modulus for a perfectly rigid body are infinite.
- Therefore, the correct answer to the question is: **Young's modulus is infinite and Bulk modulus is infinite**.

### Final Answer:
- The correct option is: Young's modulus is infinite and Bulk modulus is also infinite.