Which one of the following has the dimensions of pressure?

Options

A. `(ML)/(T^2)`
B. `M/(L^2T^2)`
C. `M/(LT^2)`
D. `M/(LT)`

Explanation

To determine which option has the dimensions of pressure, we can follow these steps:

### Step 1: Understand the definition of pressure
Pressure (P) is defined as force (F) 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 as mass times acceleration. The dimensional formula for force can be derived as follows:
- Mass (M) has the dimension [M].
- Acceleration (a) is defined as the change in velocity per unit time. Velocity has the dimension of length per time, so acceleration has the dimension:
\[ [a] = \frac{[L]}{[T^2]} \]
Thus, the dimensional formula for force (F) is:
\[ [F] = [M][L][T^{-2}] = [M L T^{-2}] \]

### 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, substituting the dimensional formulas of force and area into the pressure formula:
\[ P = \frac{F}{A} = \frac{[M L T^{-2}]}{[L^2]} \]

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

### Step 6: Identify the correct option
The dimensional formula for pressure is:
\[ [P] = [M L^{-1} T^{-2}] \]
Now, we can compare this with the options provided in the question. The correct option that matches this dimensional formula is:
\[ [M L^{-1} T^{-2}] \]

### Conclusion
Thus, the answer is that the dimensions of pressure are given by:
\[ [M L^{-1} T^{-2}] \]