The valve of Poisson's ratio lies between

Options

A. `-1` to `(1)/(2)`
B. `-(3)/(4)` to `-(1)/(2)`
C. `-(1)/(2)` to 1
D. 1 to 2

Answer

To find the range of Poisson's ratio (σ), we can follow these steps:

### Step 1: Understand Poisson's Ratio
Poisson's ratio (σ) is defined as the negative ratio of transverse to axial strain when a material is deformed elastically. It is a measure of how much a material deforms in the direction perpendicular to the applied load.

### Step 2: Identify the Theoretical Limits
Theoretical limits for Poisson's ratio are:
- For most materials, σ ranges from 0 to 0.5.
- For some materials, particularly those that are incompressible, σ can approach 0.5.
- In some cases, σ can be negative, which is observed in auxetic materials.

### Step 3: Establish the Range
From the theoretical limits, we can conclude:
- The minimum value of σ is -1 (for certain materials).
- The maximum value of σ is 0.5 (for most elastic materials).

Thus, we can state that:
\[ -1 < \sigma < 0.5 \]

### Step 4: Conclusion
Therefore, the value of Poisson's ratio lies between -1 and 0.5.

### Final Answer
The value of Poisson's ratio lies between -1 and 0.5.

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