Young's modulus of a substance depends of

Options

A. its length
B. its area
C. acceleraton due to gravity
D. none of the above

Answer

To determine the factors on which Young's modulus depends, we can analyze the definition and characteristics of Young's modulus step by step.

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (E) is defined as the ratio of stress to strain in a material within its elastic limit. Mathematically, it is expressed as:
\[ E = \frac{\text{Stress}}{\text{Strain}} \]
where stress is defined as force per unit area (F/A) and strain is the relative change in length (ΔL/L).

2. **Defining Stress and Strain**:
- **Stress**:
\[ \text{Stress} = \frac{F}{A} \]
where F is the force applied and A is the cross-sectional area.
- **Strain**:
\[ \text{Strain} = \frac{\Delta L}{L} \]
where ΔL is the change in length and L is the original length.

3. **Analyzing the Dependence**:
- From the formula for Young's modulus, we can see that it is a ratio of stress to strain.
- Stress depends on the applied force and the area, while strain depends on the change in length relative to the original length.
- Importantly, Young's modulus is a material property, meaning it is intrinsic to the material itself and does not depend on the dimensions (length or area) of the material sample.

4. **Conclusion**:
Young's modulus depends on the material's properties, such as its molecular structure and bonding, but it does not depend on the length of the specimen, the cross-sectional area, or the acceleration due to gravity. Therefore, the correct answer is that Young's modulus depends on the substance itself.

### Final Answer:
Young's modulus of a substance depends on the material's properties (the substance) and not on its length, area, or acceleration due to gravity.

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