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 determine what Young's modulus of a wire depends on, we can follow these steps:

### Step 1: Understand Young's Modulus
Young's modulus (E) is defined as the ratio of stress to strain in a material. Stress is the force applied per unit area, and strain is the deformation experienced by the material in response to the applied stress.

### Step 2: Define Stress and Strain
- **Stress (σ)** is given by the formula:
\[ \sigma = \frac{F}{A} \]
where \( F \) is the applied force and \( A \) is the cross-sectional area of the wire.

- **Strain (ε)** is defined as the change in length (ΔL) divided by the original length (L0):
\[ \epsilon = \frac{\Delta L}{L_0} \]

### Step 3: Write the Formula for Young's Modulus
Using the definitions of stress and strain, Young's modulus can be expressed as:
\[ E = \frac{\sigma}{\epsilon} = \frac{F/A}{\Delta L/L_0} \]

### Step 4: Analyze the Dependence of Young's Modulus
From the formula, we can see that:
- Young's modulus is a property that depends on the material of the wire.
- It does not depend on the dimensions (like area or length) of the wire.
- It is an intrinsic property, meaning it is characteristic of the material itself.

### Step 5: Conclusion
Thus, Young's modulus depends solely on the material from which the wire is made, and not on its dimensions or shape.

### Final Answer
Young's modulus of a wire depends on the material of the wire.

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