Pressure has the dimensions

Options

A. `[ML^(-1)T^(-2)]`
B. `[ML^(-0)T^(-1)]`
C. `[ML^(1)T^(-1)]`
D. `[ML T^(-2)]`

Answer

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

### Step-by-Step Solution:

1. **Understanding Pressure**:
- Pressure is defined as the force applied per unit area. Mathematically, this can be expressed as:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \]

2. **Finding the Dimension of Force**:
- The unit of force is Newton (N), which can be expressed in terms of mass (kg), length (m), and time (s) as:
\[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 \]
- Therefore, the dimension of force can be written as:
\[ [\text{Force}] = [\text{Mass}] \cdot [\text{Length}] \cdot [\text{Time}]^{-2} = \text{M}^1 \text{L}^1 \text{T}^{-2} \]

3. **Finding the Dimension of Area**:
- Area is defined as length squared. Thus, the dimension of area can be expressed as:
\[ [\text{Area}] = [\text{Length}]^2 = \text{L}^2 \]

4. **Calculating the Dimension of Pressure**:
- Now, substituting the dimensions of force and area into the pressure formula:
\[ [\text{Pressure}] = \frac{[\text{Force}]}{[\text{Area}]} = \frac{\text{M}^1 \text{L}^1 \text{T}^{-2}}{\text{L}^2} \]
- Simplifying this gives:
\[ [\text{Pressure}] = \text{M}^1 \text{L}^{1-2} \text{T}^{-2} = \text{M}^1 \text{L}^{-1} \text{T}^{-2} \]

5. **Final Result**:
- Therefore, the dimensions of pressure are:
\[ [\text{Pressure}] = \text{M}^1 \text{L}^{-1} \text{T}^{-2} \]

### Conclusion:
The dimensions of pressure are \( \text{M}^1 \text{L}^{-1} \text{T}^{-2} \).