Which of the following in not the unit of surface tension ?

Options

A. `N//m`
B. `J//m^(2)`
C. `kg//s^(2)`
D. None of these

Answer

To determine which of the following is not a unit of surface tension, we first need to understand what surface tension is and how it is measured.

### 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. Mathematically, it is expressed as:
\[ \text{Surface Tension} (\gamma) = \frac{F}{L} \]
where \( F \) is the force and \( L \) is the length.

2. **Units of Surface Tension**:
- The SI unit of force is Newton (N), and the SI unit of length is meter (m). Therefore, the unit of surface tension can be expressed as:
\[ \text{Unit of Surface Tension} = \frac{\text{Newton}}{\text{meter}} = \text{N/m} \]

3. **Dimensional Analysis**:
- The dimension of force (F) is given by:
\[ [F] = MLT^{-2} \]
- The dimension of length (L) is:
\[ [L] = L \]
- Therefore, the dimension of surface tension becomes:
\[ [\gamma] = \frac{MLT^{-2}}{L} = MT^{-2} \]

4. **Alternative Units**:
- We can also express surface tension in other units. For example:
- Joules (J) is defined as \( \text{N} \cdot \text{m} \) (force times distance). Thus:
\[ \text{Joules per meter squared} = \frac{\text{N} \cdot \text{m}}{\text{m}^2} = \frac{\text{N}}{\text{m}} = \text{N/m} \]
- Therefore, Joules per meter squared (J/m²) is also a unit of surface tension.

5. **Identifying Incorrect Options**:
- Now we need to evaluate the given options to identify which one is not a unit of surface tension.
- Based on our analysis, we know that:
- N/m is a valid unit.
- J/m² is a valid unit.
- kg/(s²) can be derived from N (since 1 N = kg·m/s²), but it does not represent surface tension directly.
- Therefore, the only option that does not represent a unit of surface tension is kg/(s²).

6. **Conclusion**:
- After evaluating all options, the answer to the question "Which of the following is not a unit of surface tension?" is **kg/(s²)**.