Which of the following do not have unit?

Options

A. Stess
B. Strain
C. Youngs modulus
D. All

Explanation

To determine which of the following do not have a unit—stress, strain, or Young's modulus—we can analyze each term step by step.

### Step 1: Understanding Stress
- **Definition**: Stress is defined as the force applied per unit area.
- **Formula**: Stress = Force / Area
- **Units**:
- Force is measured in Newtons (N).
- Area is measured in square meters (m²).
- **Calculation**: Therefore, the unit of stress is:
\[ \text{Unit of Stress} = \frac{\text{Force}}{\text{Area}} = \frac{N}{m^2} = \text{Pascal (Pa)} \]
- **Conclusion**: Stress has a unit.

### Step 2: Understanding Strain
- **Definition**: Strain is defined as the change in length divided by the original length.
- **Formula**: Strain = Change in Length / Original Length
- **Units**:
- Both change in length and original length are measured in meters (m) or centimeters (cm).
- **Calculation**: Therefore, strain is a ratio of two lengths:
\[ \text{Unit of Strain} = \frac{\text{Length}}{\text{Length}} = \text{unitless} \]
- **Conclusion**: Strain does not have a unit.

### Step 3: Understanding Young's Modulus
- **Definition**: Young's modulus is defined as the ratio of stress to strain.
- **Formula**: Young's Modulus = Stress / Strain
- **Units**:
- Stress has units of Pascal (Pa) or N/m².
- Strain is unitless.
- **Calculation**: Therefore, the unit of Young's modulus is:
\[ \text{Unit of Young's Modulus} = \frac{\text{Stress}}{\text{Strain}} = \frac{N/m^2}{\text{unitless}} = N/m^2 = \text{Pascal (Pa)} \]
- **Conclusion**: Young's modulus has a unit.

### Final Conclusion
Among stress, strain, and Young's modulus:
- **Stress**: Has a unit (Pascal).
- **Strain**: Does not have a unit (unitless).
- **Young's Modulus**: Has a unit (Pascal).

Thus, the answer to the question is that **strain does not have a unit**.