The dimensions `ML^-1T^-2` may correspond to

Options

A. work done by a force
B. linear momentum
C. pressure
D. energy per unt volume

Answer

To determine which physical quantities correspond to the dimensions \( ML^{-1}T^{-2} \), we will analyze each option step by step.

### Step 1: Analyze Work Done by a Force
- **Formula**: Work done \( W = \text{Force} \times \text{Displacement} \)
- **Force**: \( F = \text{mass} \times \text{acceleration} = m \cdot (l \cdot t^{-2}) = m \cdot l \cdot t^{-2} \)
- **Displacement**: \( d = l \)
- **Dimensions of Work**:
\[ W = F \cdot d = (m \cdot l \cdot t^{-2}) \cdot l = m \cdot l^2 \cdot t^{-2} = ML^2T^{-2} \]
- **Conclusion**: This does not match \( ML^{-1}T^{-2} \). So, **Option 1 is incorrect**.

### Step 2: Analyze Linear Momentum
- **Formula**: Linear momentum \( p = \text{mass} \times \text{velocity} \)
- **Mass**: \( m \)
- **Velocity**: \( v = l \cdot t^{-1} \)
- **Dimensions of Linear Momentum**:
\[ p = m \cdot v = m \cdot (l \cdot t^{-1}) = m \cdot l \cdot t^{-1} = MLT^{-1} \]
- **Conclusion**: This does not match \( ML^{-1}T^{-2} \). So, **Option 2 is incorrect**.

### Step 3: Analyze Pressure
- **Formula**: Pressure \( P = \frac{\text{Force}}{\text{Area}} \)
- **Force**: \( F = m \cdot (l \cdot t^{-2}) = m \cdot l \cdot t^{-2} \)
- **Area**: \( A = l^2 \)
- **Dimensions of Pressure**:
\[ P = \frac{F}{A} = \frac{m \cdot l \cdot t^{-2}}{l^2} = m \cdot l^{-1} \cdot t^{-2} = ML^{-1}T^{-2} \]
- **Conclusion**: This matches \( ML^{-1}T^{-2} \). So, **Option 3 is correct**.

### Step 4: Analyze Energy per Unit Volume
- **Energy**: The dimensions of energy are the same as work, which is \( ML^2T^{-2} \).
- **Volume**: \( V = l^3 \)
- **Dimensions of Energy per Unit Volume**:
\[ \text{Energy per unit volume} = \frac{ML^2T^{-2}}{L^3} = ML^{-1}T^{-2} \]
- **Conclusion**: This matches \( ML^{-1}T^{-2} \). So, **Option 4 is correct**.

### Final Conclusion
The dimensions \( ML^{-1}T^{-2} \) correspond to:
- **Option 3: Pressure**
- **Option 4: Energy per unit volume**