Young's modulus of a wire depends on

Options

A. diameter of the wire
B. mass hanging from the wire
C. length of the wire
D.  material of the wire

Explanation

To answer the question "Young's modulus of a wire depends on," we need to analyze the factors that influence Young's modulus.

### Step-by-Step Solution:

1. **Definition of Young's Modulus**:
Young's modulus (E) is defined as the ratio of stress (σ) to strain (ε) in a material. Mathematically, it is expressed as:
\[ E = \frac{\sigma}{\epsilon} \]

2. **Understanding Stress and Strain**:
- **Stress (σ)** is defined as the force (F) applied per unit area (A) of the material:
\[ \sigma = \frac{F}{A} \]
- **Strain (ε)** is the measure of deformation representing the displacement between particles in a material body:
\[ \epsilon = \frac{\Delta L}{L_0} \]
where \( \Delta L \) is the change in length and \( L_0 \) is the original length.

3. **Factors Affecting Young's Modulus**:
- **Material Properties**: Young's modulus is an intrinsic property of the material itself. Different materials have different Young's moduli based on their atomic structure and bonding.
- **Temperature**: The Young's modulus can change with temperature. Generally, as temperature increases, the Young's modulus decreases.
- **Microstructure**: The arrangement of atoms, grain size, and phase of the material can also affect Young's modulus.

4. **Conclusion**:
Young's modulus depends primarily on the material of the wire and its temperature. It does not depend on the dimensions (length, diameter) of the wire or the amount of load applied.

### Final Answer:
Young's modulus of a wire depends on the material properties and temperature.