The correct statement about poisson's ratio is

Options

A. Its unit of Newton
B. Its dimension are `MLT^(-2)`
C. Its unit is `Nm^(-2)`
D. It is dimensions

Answer

To solve the question regarding Poisson's ratio, let's break it down step by step.

### Step 1: Understand Poisson's Ratio
Poisson's ratio (ν) is defined as the ratio of lateral strain to longitudinal strain.

### Step 2: Define Strain
Strain is a measure of deformation representing the displacement between particles in a material body. It is defined mathematically as:
- Longitudinal strain (ε_long) = ΔL / L
- Lateral strain (ε_lat) = Δθ / θ

Where:
- ΔL = change in length
- L = original length
- Δθ = change in diameter (or lateral dimension)
- θ = original diameter (or lateral dimension)

### Step 3: Analyze the Dimensions
Both longitudinal strain and lateral strain are dimensionless quantities because they are ratios of lengths (change in length/original length).

### Step 4: Calculate Poisson's Ratio
Poisson's ratio is given by:
\[ ν = \frac{ε_{lat}}{ε_{long}} = \frac{\Delta \theta / \theta}{\Delta L / L} \]

Since both ε_lat and ε_long are dimensionless, their ratio (Poisson's ratio) is also dimensionless.

### Step 5: Conclusion
Thus, Poisson's ratio is a dimensionless quantity.

### Final Answer
The correct statement about Poisson's ratio is that it is dimensionless.

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