Thd dimensional formula of pressure is

Options

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

Explanation

To find the dimensional formula of pressure, we start with the definition of pressure and the dimensional formulas of the quantities involved.

### Step-by-Step Solution:

1. **Understanding Pressure**:
Pressure (P) is defined as the force (F) applied per unit area (A). Mathematically, this is expressed as:
\[ P = \frac{F}{A} \]

2. **Dimensional Formula of Force**:
Force is given by Newton's second law, which states that force is the product of mass (m) and acceleration (a):
\[ F = m \cdot a \]
The dimensional formula for mass (m) is \( [M] \). Acceleration (a) is defined as the change in velocity per unit time. The dimensional formula for velocity is \( [L T^{-1}] \), so the dimensional formula for acceleration is:
\[ a = \frac{[L T^{-1}]}{[T]} = [L T^{-2}] \]
Therefore, the dimensional formula for force becomes:
\[ F = [M] \cdot [L T^{-2}] = [M L T^{-2}] \]

3. **Dimensional Formula of Area**:
Area (A) is defined as length squared. The dimensional formula for length is \( [L] \), so the dimensional formula for area is:
\[ A = [L^2] \]

4. **Combining to Find Dimensional Formula of Pressure**:
Now, substituting the dimensional formulas of force and area into the formula for pressure:
\[ P = \frac{F}{A} = \frac{[M L T^{-2}]}{[L^2]} \]
Simplifying this gives:
\[ P = [M L T^{-2}] \cdot [L^{-2}] = [M L^{1-2} T^{-2}] = [M L^{-1} T^{-2}] \]

5. **Final Result**:
The dimensional formula of pressure is:
\[ [M L^{-1} T^{-2}] \]

### Conclusion:
The correct dimensional formula for pressure is \( [M L^{-1} T^{-2}] \).