Which one the following is not a unit of Young's modulus ?

Options

A. `Nm^(-1)`
B. `Nm^(-2)`
C. Dyne `cm^(-2)`
D. Mega pascal

Explanation

To determine which of the following is not a unit of Young's modulus, we first need to understand what Young's modulus is and how it is defined.

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (E) is a measure of the stiffness of a solid material. It is defined as the ratio of stress (force per unit area) to strain (deformation relative to original length).

2. **Formula for Young's Modulus**:
\[ E = \frac{\text{Stress}}{\text{Strain}} \]

3. **Units of Stress**:
- Stress is defined as force per unit area.
- The SI unit of force is Newton (N).
- The SI unit of area is square meters (m²).
- Therefore, the unit of stress is:
\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{N}{m^2} = \text{Pascals (Pa)} \]

4. **Units of Strain**:
- Strain is a dimensionless quantity (it is the ratio of change in length to original length), so it has no units.

5. **Combining Units for Young's Modulus**:
- Since strain is unitless, the units of Young's modulus are the same as the units of stress:
\[ E = \text{Stress} = \frac{N}{m^2} = \text{Pascals (Pa)} \]

6. **Alternative Units**:
- In CGS (centimeter-gram-second) units, force is measured in dynes (dyn) and area in square centimeters (cm²). Thus, the unit can also be expressed as:
\[ E = \frac{\text{dyn}}{\text{cm}^2} \]
- Additionally, 1 Pascal = 1 N/m² = 10⁶ dyn/cm², which means that Young's modulus can also be expressed in megapascals (MPa), where:
\[ 1 \text{ MPa} = 10^6 \text{ Pa} \]

7. **Identifying the Incorrect Unit**:
- From the information above, valid units of Young's modulus include:
- Pascals (Pa)
- Newton per square meter (N/m²)
- Dynes per square centimeter (dyn/cm²)
- Megapascals (MPa)
- The option that is not a unit of Young's modulus is "Newton meter (N·m)", which is a unit of torque, not stress.

### Conclusion:
Thus, the answer is that "Newton meter" is not a unit of Young's modulus.

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