Which are not suitable units for surface tension in S.I. system

Options

A. `Kg.m^(-1)S^(-1)`
B. `Kg.S^(-1)`
C. `N.m^(-1)`
D. `J.m^(-1)`

Answer

To determine which units are not suitable for measuring surface tension in the SI system, we first need to understand what surface tension is and its appropriate units.

### Step-by-Step Solution:

1. **Understanding Surface Tension**:
- Surface tension is defined as the force acting along the surface of a liquid per unit length. It is a measure of how much force is required to stretch or break the surface of a liquid.

2. **Mathematical Expression**:
- The formula for surface tension (γ) can be expressed as:
\[ \gamma = \frac{F}{L} \]
where \( F \) is the force acting normal to a line of unit length along the surface, and \( L \) is the length of that line.

3. **Units of Force and Length**:
- In the SI system, the unit of force (F) is Newton (N), and the unit of length (L) is meter (m).

4. **Calculating the SI Unit of Surface Tension**:
- Therefore, the SI unit of surface tension is:
\[ \text{Surface Tension} = \frac{\text{Newton}}{\text{meter}} = \text{N/m} \]

5. **Identifying Unsuitable Units**:
- Any unit that does not conform to the expression of force per unit length (N/m) would be considered unsuitable for measuring surface tension. Examples of unsuitable units could include:
- Pascal (Pa) - which is a unit of pressure (N/m²).
- Joules (J) - which is a unit of energy (N·m).
- Any arbitrary units that do not represent a force per unit length.

### Conclusion:
The suitable unit for surface tension in the SI system is Newton per meter (N/m). Any units that do not represent this ratio, such as Pascal (Pa) or Joules (J), are not suitable for measuring surface tension.