The dimensions of pressure are

Options

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

Answer

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

### Step 1: Understand the Definition of Pressure
Pressure is defined as the force applied per unit area. Mathematically, this can be expressed as:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \]

### Step 2: Identify the Dimensions of Force
The dimensions of force can be derived from Newton's second law, which states that force is equal to mass times acceleration. The formula for force is:
\[ \text{Force} = \text{Mass} \times \text{Acceleration} \]
The dimensions of mass (M) are simply \( M \). The dimensions of acceleration (A) are given by:
\[ \text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}} = \frac{L T^{-1}}{T} = L T^{-2} \]
Thus, the dimensions of force (F) are:
\[ [F] = M \cdot (L T^{-2}) = M L T^{-2} \]

### Step 3: Identify the Dimensions of Area
The area (A) is defined as the length squared. Therefore, the dimensions of area are:
\[ [A] = L^2 \]

### Step 4: Calculate the Dimensions of Pressure
Now that we have both the dimensions of force and area, we can find the dimensions of pressure:
\[ [P] = \frac{[F]}{[A]} = \frac{M L T^{-2}}{L^2} \]
When we simplify this expression:
\[ [P] = M L^{-1} T^{-2} \]

### Step 5: Conclusion
The dimensions of pressure are:
\[ [P] = M L^{-1} T^{-2} \]

### Final Answer
The dimensions of pressure are \( M L^{-1} T^{-2} \).

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