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. Different stresses and strains
B. The same stress and strain
C. The same strain but different stresses
D. The same stress but different strains

Explanation

To solve the problem step by step, we need to analyze the situation involving the copper wire and steel wire connected end to end under the application of a force.

### Step 1: Understand the Setup
We have two wires: one made of copper and the other made of steel. Both wires have the same diameter and length and are connected end to end. When a force is applied to the combined wires, they stretch by a total of 1 cm.

### Step 2: Identify Key Concepts
1. **Stress (σ)**: Stress is defined as the force (F) applied per unit area (A). It can be expressed as:
\[ \sigma = \frac{F}{A} \]
2. **Strain (ε)**: Strain is defined as the change in length (ΔL) divided by the original length (L). It can be expressed as:
\[ \epsilon = \frac{\Delta L}{L} \]
3. **Young's Modulus (Y)**: Young's modulus relates stress and strain for a material:
\[ Y = \frac{\sigma}{\epsilon} \]

### Step 3: Analyzing the Stress
Since both wires have the same diameter, their cross-sectional areas are identical. When the same force is applied to both wires, the stress in both wires will be the same:
\[ \sigma_{\text{copper}} = \sigma_{\text{steel}} = \frac{F}{A} \]

### Step 4: Analyzing the Strain
The strain in each wire is dependent on Young's modulus, which is different for copper and steel. Therefore, even though the stress is the same, the strains will differ due to the different material properties:
\[ \epsilon_{\text{copper}} = \frac{\sigma_{\text{copper}}}{Y_{\text{copper}}} \]
\[ \epsilon_{\text{steel}} = \frac{\sigma_{\text{steel}}}{Y_{\text{steel}}} \]

### Step 5: Conclusion
Since the stress is the same for both wires but the Young's moduli are different, the strains must also be different. Thus, we conclude that:
- The stress in both wires is the same.
- The strain in both wires is different.

### Final Answer
The correct option is: **Same stress but different strain.**

---