Dimensional formula `ML^(-1)T^2` does not represent the physical quantity

Options

A. young's modulus of elasticity
B. stress
C. strain
D. pressure

Explanation

To determine which physical quantity does not have the dimensional formula \( ML^{-1}T^{-2} \), we will analyze the dimensions of Young's modulus, stress, strain, and pressure.

### Step-by-Step Solution:

1. **Understanding the Given Dimensional Formula**:
The dimensional formula we are examining is \( ML^{-1}T^{-2} \). We need to find a physical quantity that does not match this dimensional formula.

2. **Analyzing Young's Modulus**:
- **Definition**: Young's modulus (Y) is defined as the ratio of stress to strain.
- **Stress**: Stress is defined as force per unit area.
\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A} \]
The dimension of force (F) is \( ML T^{-2} \) and the dimension of area (A) is \( L^2 \).
\[ \text{Dimension of Stress} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} \]
- **Strain**: Strain is defined as the change in length divided by the original length, which is dimensionless.
\[ \text{Strain} = \frac{\Delta L}{L} \implies \text{Dimension of Strain} = L^0 \]
- Therefore, the dimension of Young's modulus is:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{ML^{-1}T^{-2}}{L^0} = ML^{-1}T^{-2} \]

3. **Analyzing Stress**:
- As calculated above, the dimension of stress is:
\[ \text{Dimension of Stress} = ML^{-1}T^{-2} \]

4. **Analyzing Strain**:
- As calculated above, the dimension of strain is:
\[ \text{Dimension of Strain} = L^0 \]
- This shows that strain is dimensionless and does not match \( ML^{-1}T^{-2} \).

5. **Analyzing Pressure**:
- **Definition**: Pressure is also defined as force per unit area.
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A} \]
- As calculated earlier, the dimension of pressure is:
\[ \text{Dimension of Pressure} = ML^{-1}T^{-2} \]

6. **Conclusion**:
Among the quantities analyzed, strain is the only one that does not have the dimensional formula \( ML^{-1}T^{-2} \). Therefore, the answer is strain.

### Final Answer:
The physical quantity that does not represent the dimensional formula \( ML^{-1}T^{-2} \) is **strain**.