A Copper wire and steel of the same diameter and length are connected end to end and a force is applied, which stretches their combined length by 1 cm. The two wires will have

Options

A. the same stress and strain
B. the same stress but different strain
C. the same strain but different stress
D. different strains and stress

Explanation

To solve the problem, we need to analyze the behavior of the copper and steel wires when a force is applied to them. Here’s a step-by-step solution:

### Step 1: Understand the Setup
We have two wires (copper and steel) connected end to end. Both wires have the same diameter and length. When a force is applied, the combined length of the wires stretches by 1 cm.

### Step 2: Identify Key Concepts
- **Stress (σ)** is defined as the force (F) applied per unit area (A):
\[ \sigma = \frac{F}{A} \]
- **Strain (ε)** is defined as the change in length (ΔL) divided by the original length (L):
\[ \epsilon = \frac{\Delta L}{L} \]
- The relationship between stress and strain is given by Hooke's Law, which states that stress is proportional to strain for elastic materials:
\[ \sigma = E \cdot \epsilon \]
where E is the modulus of elasticity (Young's modulus) of the material.

### Step 3: Analyze the Forces
Since both wires are connected end to end and are subjected to the same force, the force applied on both the copper and steel wires is equal:
\[ F_{copper} = F_{steel} = F \]

### Step 4: Calculate Stress
Since both wires have the same diameter, their cross-sectional areas are equal. Thus, the stress in both wires is the same:
\[ \sigma_{copper} = \sigma_{steel} = \frac{F}{A} \]

### Step 5: Calculate Strain
The strain in each wire will depend on the material properties (Young's modulus). Since the Young's modulus for copper (E_copper) and steel (E_steel) are different, the strains in the two wires will be different:
\[ \epsilon_{copper} = \frac{\sigma_{copper}}{E_{copper}} \quad \text{and} \quad \epsilon_{steel} = \frac{\sigma_{steel}}{E_{steel}} \]
Given that the stress is the same for both, we can conclude:
\[ \epsilon_{copper} \neq \epsilon_{steel} \]

### Step 6: Conclusion
Since both wires experience the same stress but have different strains due to their different material properties, the correct answer is:
- **The same stress but different strain.**

### Final Answer
The two wires will have the same stress but different strain.

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