Question

A copper and a steel wire of the same diameter are connected end to end. A deforming force F is applied to this composite wire which causes a total elongation of 3 cm. The two wires will have

• A. the same stress and different strain.
• B. the same strain and different stress.
• C. the same stress and same strain.
• D. different stress and different strain.

Hint:

Series connection = Same Force. Same Diameter = Same Area. Therefore, Stress is identical.

Answer 1

The Correct Option is A

Step 1: Concept
Stress is defined as Force/Area ($\sigma = F/A$). Strain is defined as the change in length over original length ($\epsilon = \Delta L/L$).

Step 2: Analysis
Since the wires are connected in series (end-to-end), the same deforming force $F$ acts on both. Because they have the same diameter, their cross-sectional areas are identical.

Step 3: Reasoning
Equal force and equal area result in equal stress. However, steel and copper have different Young's Moduli ($Y$). Since $\epsilon = \text{stress} / Y$, the strains must be different.

Step 4: Conclusion
The wires experience identical stress but different strain due to differing material properties. Final Answer: (A)