The correct statement about poisson's ratio is

Options

A. (a)Its unit of Newton
B. (b)Its dimension are `MLT^(-2)`
C. (c)Its unit is `Nm^(-2)`
D. (d)It is dimensionless

Answer

To solve the question regarding Poisson's ratio, we will follow these steps:

### Step 1: Understand Poisson's Ratio
Poisson's ratio (denoted as \( \nu \)) is defined as the ratio of lateral strain to longitudinal strain when a material is subjected to stress.

### Step 2: Define Strains
- **Lateral Strain**: This is the strain that occurs in the direction perpendicular to the applied load.
- **Longitudinal Strain**: This is the strain that occurs in the direction of the applied load.

### Step 3: Write the Formula
The formula for Poisson's ratio is given by:
\[ \nu = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} \]
The negative sign indicates that when a material is stretched (longitudinal strain), it tends to contract in the lateral direction.

### Step 4: Identify the Properties of Poisson's Ratio
- Poisson's ratio is a dimensionless quantity because it is a ratio of two strains (both of which are dimensionless).
- It does not have units of mass, length, or time.

### Step 5: Analyze the Options
Given the options A, B, C, and D, we need to identify which one correctly describes Poisson's ratio. Based on our understanding:
- The correct statement should mention that Poisson's ratio is a dimensionless quantity.

### Step 6: Conclusion
After analyzing the options, we find that option D is the correct statement about Poisson's ratio.

### Final Answer
The correct statement about Poisson's ratio is: **It is a dimensionless quantity.**

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