"Pascal-Second" has dimension of

Options

A. Force
B. Energy
C. Pressure
D. Coefficient of viscosity

Answer

To find the dimension of "Pascal-Second," we need to break down the units involved.

### Step-by-Step Solution:

1. **Understanding Pascal**:
- Pascal (Pa) is the unit of pressure, defined as one Newton per square meter (N/m²).
- Therefore, we can express Pascal as:
\[ \text{Pascal} = \frac{\text{Force}}{\text{Area}} = \frac{\text{N}}{\text{m}^2} \]

2. **Expressing Newton in terms of base units**:
- Newton (N) is the unit of force, which can be expressed as:
\[ \text{N} = \text{kg} \cdot \text{m/s}^2 \]
- Thus, we can rewrite Pascal as:
\[ \text{Pascal} = \frac{\text{kg} \cdot \text{m/s}^2}{\text{m}^2} = \frac{\text{kg}}{\text{m} \cdot \text{s}^2} \]

3. **Combining Pascal with Seconds**:
- Now we need to find the dimension of Pascal-Second (Pa·s):
\[ \text{Pascal-Second} = \text{Pascal} \times \text{Second} = \left(\frac{\text{kg}}{\text{m} \cdot \text{s}^2}\right) \times \text{s} \]

4. **Simplifying the Expression**:
- When we multiply Pascal by seconds, we have:
\[ \text{Pascal-Second} = \frac{\text{kg}}{\text{m} \cdot \text{s}^2} \times \text{s} = \frac{\text{kg}}{\text{m} \cdot \text{s}} \]

5. **Final Result**:
- Therefore, the dimension of Pascal-Second is:
\[ [\text{Pascal-Second}] = \frac{\text{kg}}{\text{m} \cdot \text{s}} = \text{M} \cdot \text{L}^{-1} \cdot \text{T}^{-1} \]

### Final Answer:
The dimension of "Pascal-Second" is \(\text{M} \cdot \text{L}^{-1} \cdot \text{T}^{-1}\).

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