Which of the following is not represented in correct unit

Options

A. `"Stress"/"Strain"=N//m^2`
B. Surface tension=N/m
C. Energy= kg-m/s
D. Pressure=`N//m^2`

Answer

To determine which of the given options is not represented in the correct unit, we will analyze each option step by step.

### Step 1: Analyze the first option - Stress
- **Definition**: Stress is defined as force per unit area.
- **Units**:
- Force (F) is measured in Newtons (N).
- Area (A) is measured in square meters (m²).
- **Unit of Stress**:
\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{N}{m^2} \]
- **Conclusion**: The unit of stress is correctly represented as Newton per meter square (N/m²).

### Step 2: Analyze the second option - Surface Tension
- **Definition**: Surface tension is defined as force per unit length.
- **Units**:
- Force (F) is measured in Newtons (N).
- Length (L) is measured in meters (m).
- **Unit of Surface Tension**:
\[ \text{Surface Tension} = \frac{\text{Force}}{\text{Length}} = \frac{N}{m} \]
- **Conclusion**: The unit of surface tension is correctly represented as Newton per meter (N/m).

### Step 3: Analyze the third option - kg per kg meter per second
- **Expression**: The expression given is kg/(kg·m/s).
- **Analysis**:
- The unit of energy (or work) is Joules (J), which can be expressed as:
\[ \text{Energy} = \text{Force} \times \text{Distance} = N \cdot m = \frac{kg \cdot m}{s^2} \cdot m = \frac{kg \cdot m^2}{s^2} \]
- **Incorrect Representation**: The given unit kg/(kg·m/s) simplifies to:
\[ \frac{kg}{kg \cdot m/s} = \frac{1}{m/s} = \frac{s}{m} \]
This is not a correct representation of energy or work.
- **Conclusion**: This option is not represented in the correct unit.

### Step 4: Analyze the fourth option - Pressure
- **Definition**: Pressure is defined as force per unit area.
- **Units**:
- Force (F) is measured in Newtons (N).
- Area (A) is measured in square meters (m²).
- **Unit of Pressure**:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{N}{m^2} \]
- **Conclusion**: The unit of pressure is correctly represented as Newton per meter square (N/m²).

### Final Conclusion
Among the options analyzed, the third option (kg per kg meter per second) is not represented in the correct unit.

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