The ratio of the change in dimension at right angles to the applied force to the initial dimension is known as

Options

A. Young's modulus
B. Poisson's ratio
C. Lateral strain
D. Shearing strain

Answer

To solve the question, "The ratio of the change in dimension at right angles to the applied force to the initial dimension is known as," we need to understand the concepts of strain and how they relate to the application of force on a material.

### Step-by-Step Solution:

1. **Understanding the Applied Force**:
- When a force is applied to a material, it can cause changes in its dimensions. If we apply a tensile force along the length of a cylindrical wire, the length of the wire increases.

2. **Defining Longitudinal Strain**:
- The change in length (extension) of the wire due to the applied force is referred to as longitudinal strain. It is defined as:
\[ \text{Longitudinal Strain} = \frac{\Delta L}{L_0} \]
where \( \Delta L \) is the change in length and \( L_0 \) is the original length.

3. **Understanding Lateral Dimensions**:
- When the length of the wire increases, the dimensions at right angles to the applied force (the lateral dimensions) will decrease. This is due to the material's tendency to conserve volume.

4. **Defining Lateral Strain**:
- The change in dimension at right angles to the applied force is known as lateral strain. It is defined as:
\[ \text{Lateral Strain} = \frac{\Delta D}{D_0} \]
where \( \Delta D \) is the change in diameter (or lateral dimension) and \( D_0 \) is the original diameter.

5. **Relating Lateral Strain to Poisson's Ratio**:
- The ratio of lateral strain to longitudinal strain is known as Poisson's ratio (\( \nu \)). It can be expressed as:
\[ \nu = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} = -\frac{\Delta D / D_0}{\Delta L / L_0} \]
- This indicates how much the lateral dimension changes in response to the longitudinal strain.

6. **Conclusion**:
- The ratio of the change in dimension at right angles to the applied force to the initial dimension is known as **Lateral Strain**.

### Final Answer:
The ratio of the change in dimension at right angles to the applied force to the initial dimension is known as **Lateral Strain**.