Which of the following is dimensionally correct?

Options

A. pressure`=`energy per unit area
B. `pressure`=`energy per unit volume
C. pressure`=`force per unit volume
D. pressure `=`momentum per unit volume per unit time

Explanation

To determine which of the given options is dimensionally correct, we need to analyze each option and compare its dimensions with the dimension of pressure.

### Step-by-Step Solution:

1. **Understand the Dimension of Pressure**:
- Pressure is defined as force per unit area.
- The dimension of force is given by \( [F] = MLT^{-2} \).
- The dimension of area is given by \( [A] = L^2 \).
- Therefore, the dimension of pressure \( [P] \) can be calculated as:
\[ [P] = \frac{[F]}{[A]} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} \]

2. **Analyze Each Option**:
- **Option A: Energy per unit area**:
- The dimension of energy is \( [E] = ML^2T^{-2} \).
- The dimension of area is \( [A] = L^2 \).
- Therefore, the dimension of energy per unit area is:
\[ \frac{[E]}{[A]} = \frac{ML^2T^{-2}}{L^2} = ML^0T^{-2} = MT^{-2} \]
- This is not equal to \( ML^{-1}T^{-2} \), so Option A is incorrect.

- **Option B: Energy per unit volume**:
- The dimension of volume is \( [V] = L^3 \).
- Therefore, the dimension of energy per unit volume is:
\[ \frac{[E]}{[V]} = \frac{ML^2T^{-2}}{L^3} = ML^{-1}T^{-2} \]
- This matches the dimension of pressure, so Option B is correct.

- **Option C: Force per unit volume**:
- The dimension of force is \( [F] = MLT^{-2} \).
- Therefore, the dimension of force per unit volume is:
\[ \frac{[F]}{[V]} = \frac{MLT^{-2}}{L^3} = ML^{-2}T^{-2} \]
- This is not equal to \( ML^{-1}T^{-2} \), so Option C is incorrect.

- **Option D: Momentum per unit volume per unit time**:
- Momentum is defined as \( [p] = [m][v] = MLT^{-1} \).
- Therefore, the dimension of momentum per unit volume per unit time is:
\[ \frac{[p]}{[V][T]} = \frac{MLT^{-1}}{L^3 \cdot T} = \frac{ML^{-2}T^{-1}}{T} = ML^{-2}T^{-2} \]
- This is not equal to \( ML^{-1}T^{-2} \), so Option D is incorrect.

3. **Conclusion**:
- The only option that has the same dimension as pressure is **Option B: Energy per unit volume**.

### Final Answer:
**Option B** is dimensionally correct.