"Pascal-Second" has dimension of

Options

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

Answer

To determine the dimension of "Pascal-Second," we will follow these steps:

### Step 1: Understand the Unit "Pascal"
Pascal (Pa) is the SI unit of pressure. It is defined as one newton per square meter.
\[ 1 \text{ Pascal} = 1 \frac{\text{N}}{\text{m}^2} \]

### Step 2: Find the Dimension of Force
The dimension of force (F) is given by Newton's second law, which states that force is mass times acceleration.
\[ \text{Force} = \text{mass} \times \text{acceleration} \]
In terms of dimensions:
\[ \text{Force} = M \cdot L \cdot T^{-2} \]
Where:
- \( M \) = mass
- \( L \) = length
- \( T \) = time

### Step 3: Find the Dimension of Area
Area (A) is defined as length squared.
\[ \text{Area} = L^2 \]

### Step 4: Find the Dimension of Pressure
Using the definition of pressure:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \]
Substituting the dimensions:
\[ \text{Pressure} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} \]

### Step 5: Find the Dimension of Pascal-Second
Now, Pascal is pressure, and we need to find the dimension of Pascal-Second:
\[ \text{Pascal-Second} = \text{Pressure} \times \text{Time} \]
Substituting the dimensions:
\[ \text{Pascal-Second} = (ML^{-1}T^{-2}) \times T = ML^{-1}T^{-1} \]

### Conclusion
The dimension of Pascal-Second is:
\[ \text{Dimension of Pascal-Second} = ML^{-1}T^{-1} \]