The modulus of elasticity of a perfectly rigid body is

Options

A. zero
B. infinity
C. unity
D. a negative number

Explanation

To solve the question about the modulus of elasticity of a perfectly rigid body, we will follow these steps:

### Step 1: Understand Modulus of Elasticity
The modulus of elasticity (E) is defined as the ratio of stress (force per unit area) to strain (deformation per unit length) in a material. It indicates how much a material will deform under a given stress.

### Step 2: Define a Perfectly Rigid Body
A perfectly rigid body is an idealized material that does not deform at all when subjected to stress. This means that no matter how much force is applied, the body will not change its shape or size.

### Step 3: Analyze Strain in a Perfectly Rigid Body
Strain is defined as the change in length (ΔL) divided by the original length (L). For a perfectly rigid body, the change in length (ΔL) is zero because it does not deform. Therefore, the strain is:
\[ \text{Strain} = \frac{\Delta L}{L} = \frac{0}{L} = 0 \]

### Step 4: Calculate Modulus of Elasticity
Since the modulus of elasticity is defined as:
\[ E = \frac{\text{Stress}}{\text{Strain}} \]
And we have established that strain is zero for a perfectly rigid body, we can substitute this into the equation. However, since we cannot divide by zero, we can conclude that:
- If strain is zero, the modulus of elasticity approaches infinity.

### Step 5: Conclusion
Thus, the modulus of elasticity of a perfectly rigid body is considered to be infinite.

### Final Answer
The modulus of elasticity of a perfectly rigid body is **infinity**.

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