Which of the following are SI units of Young’s modulus?
N/m · s2
kg/m2
kg · m/s2
kg/m · s2
kg · m2/s2
The correct answer and explanation is :
The correct SI unit of Young’s modulus is N/m², which is equivalent to kg/(m·s²).
Explanation:
1. Definition of Young’s Modulus:
Young’s modulus (E) is a measure of the stiffness of a material and is defined as the ratio of stress to strain:
[
E = \frac{\text{Stress}}{\text{Strain}}
]
- Stress is force per unit area:
[
\text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{N}{m^2}
] - Strain is dimensionless (it is the ratio of change in length to original length).
Since strain has no units, the unit of Young’s modulus is the same as that of stress:
[
E = \frac{\text{N}}{m^2}
]
2. SI Unit of Force:
Force (Newton) is given by Newton’s second law:
[
F = m \cdot a
]
where:
- ( m ) is mass in kilograms (kg),
- ( a ) is acceleration in meters per second squared (m/s²).
Since acceleration has units of ( \text{m/s}^2 ), the unit of force (Newton) is:
[
1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2
]
3. SI Unit of Young’s Modulus:
Using the unit of force, Young’s modulus has the unit:
[
E = \frac{N}{m^2} = \frac{\text{kg} \cdot \text{m/s}^2}{m^2} = \frac{\text{kg}}{\text{m} \cdot \text{s}^2}
]
Thus, the correct unit from the given options is kg/(m·s²).
4. Analysis of Given Options:
- N/m·s² → Incorrect (not stress-related).
- kg/m² → Incorrect (no time dimension).
- kg·m/s² → Incorrect (this is Newton, not modulus).
- kg/m·s² → Correct.
- kg·m²/s² → Incorrect (this is Joule, unit of energy).