The dimensional formula of pressure is

Options

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

Answer

To find the dimensional formula of pressure, we can follow these steps:

### Step 1: Understand the Definition of Pressure
Pressure (P) is defined as the force (F) applied per unit area (A). Mathematically, this can be expressed as:
\[ P = \frac{F}{A} \]

### Step 2: Write the Dimensional Formula for Force
Force is defined by Newton's second law of motion, which states that force is the product of mass (m) and acceleration (a):
\[ F = m \cdot a \]

The dimensional formula for mass (m) is:
\[ [m] = M \]

Acceleration (a) is defined as the change in velocity per unit time. The dimensional formula for velocity (v) is:
\[ [v] = \frac{L}{T} \]
Thus, the dimensional formula for acceleration (a) is:
\[ [a] = \frac{L}{T^2} \]

Combining these, the dimensional formula for force (F) is:
\[ [F] = [m] \cdot [a] = M \cdot \frac{L}{T^2} = M L T^{-2} \]

### Step 3: Write the Dimensional Formula for Area
Area (A) is defined as length squared. Therefore, the dimensional formula for area is:
\[ [A] = L^2 \]

### Step 4: Substitute the Dimensional Formulas into the Pressure Formula
Now we can substitute the dimensional formulas for force and area into the formula for pressure:
\[ [P] = \frac{[F]}{[A]} = \frac{M L T^{-2}}{L^2} \]

### Step 5: Simplify the Expression
When we simplify the expression, we get:
\[ [P] = \frac{M L T^{-2}}{L^2} = M L^{1-2} T^{-2} = M L^{-1} T^{-2} \]

### Conclusion
Thus, the dimensional formula for pressure is:
\[ [P] = M L^{-1} T^{-2} \]

### Final Answer
The dimensional formula of pressure is \( M L^{-1} T^{-2} \).

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