The SI unit of a physical quantity is pascal seconds - The dimensional formula of this quantity will be :

Options

A. `[ML^(-1)T^(-1)]`
B. `[ML^(-1)T^(-2)]`
C. `[ML^(2)T^(-1)]`
D. `[M^(-1)L^(3)T^(3)]`

Explanation

To find the dimensional formula of a physical quantity whose SI unit is pascal seconds (Pa·s), we can follow these steps:

### Step 1: Identify the Unit
The unit "pascal seconds" is associated with the coefficient of viscosity. Thus, we can start by recalling that:
\[ \text{Pascal} = \frac{\text{Force}}{\text{Area}} \]
and the unit of time is seconds.

### Step 2: Express Pascal in Terms of Fundamental Units
The pascal (Pa) is defined as:
\[ 1 \text{ Pa} = \frac{1 \text{ N}}{1 \text{ m}^2} \]
where 1 Newton (N) is defined as:
\[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 \]
Thus, we can write:
\[ 1 \text{ Pa} = \frac{1 \text{ kg} \cdot \text{m/s}^2}{1 \text{ m}^2} = \frac{1 \text{ kg}}{\text{m} \cdot \text{s}^2} \]

### Step 3: Combine Units for Pascal Seconds
Now, we can express pascal seconds (Pa·s):
\[ 1 \text{ Pa·s} = \left( \frac{1 \text{ kg}}{\text{m} \cdot \text{s}^2} \right) \cdot \text{s} = \frac{1 \text{ kg}}{\text{m} \cdot \text{s}} \]

### Step 4: Write the Dimensional Formula
From the above expression, we can identify the dimensions:
- Mass (M) is represented as \( M \)
- Length (L) is represented as \( L \)
- Time (T) is represented as \( T \)

Thus, the dimensional formula for pascal seconds is:
\[ [\text{Pascal seconds}] = [M^1 L^{-1} T^{-1}] \]

### Final Answer
The dimensional formula of the physical quantity whose SI unit is pascal seconds is:
\[ [M^1 L^{-1} T^{-1}] \]

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