Which of the following is not a correct expression regarding the units of coefficient of viscosity ?

Options

A. dyne `cm^(-2) s`
B. dyne `cm^(2) s^(-1)`
C. N `m^(-2) s`
D. Pa s

Answer

To solve the question regarding the units of the coefficient of viscosity, we need to analyze the options given and determine which one is not a correct expression for the units of viscosity.

### Step-by-Step Solution:

1. **Understand Viscosity**:
- Viscosity is a measure of a fluid's resistance to flow. It indicates how easily a fluid can move or deform when subjected to an external force.

2. **Identify the Coefficient of Viscosity**:
- The coefficient of viscosity (η) can be defined through the formula:
\[ \eta = \frac{F \cdot d}{A \cdot v} \]
where:
- \( F \) = tangential force,
- \( d \) = distance between the layers,
- \( A \) = area,
- \( v \) = velocity.

3. **Derive the Units**:
- From the formula, we can derive the units of viscosity:
- Force (F) is measured in Newtons (N).
- Area (A) is measured in square meters (m²).
- Velocity (v) is measured in meters per second (m/s).
- Therefore, the unit of viscosity can be expressed as:
\[ \text{Units of } \eta = \frac{N \cdot m}{m^2 \cdot m/s} = \frac{N \cdot s}{m^2} \]
- Since \( 1 \, N = 1 \, \frac{kg \cdot m}{s^2} \), we can rewrite the unit:
\[ \eta = \frac{kg \cdot m/s^2 \cdot s}{m^2} = \frac{kg}{m \cdot s} \]
- In SI units, this can also be expressed as Pascal seconds (Pa·s), where \( 1 \, Pa = 1 \, \frac{N}{m^2} \).

4. **Identify the Correct Units**:
- The common units of viscosity include:
- Pascal seconds (Pa·s)
- Newton seconds per square meter (N·s/m²)
- Dyne seconds per square centimeter (dyn·s/cm²)

5. **Evaluate the Options**:
- Now, we will evaluate the options provided in the question:
- **Option A**: Dyn/cm²·s - This is a correct unit.
- **Option B**: Dyn·cm²/s - This is not a correct unit for viscosity.
- **Option C**: N·s/m² - This is a correct unit.
- **Option D**: Pa·s - This is a correct unit.

6. **Conclusion**:
- The option that is not a correct expression for the units of the coefficient of viscosity is **Option B**: Dyn·cm²/s.

### Final Answer:
**Option B** is not a correct expression regarding the units of the coefficient of viscosity.