Question

A copper wire and a steel wire of same length and same cross-section are joined end to end to form a composite wire. The composite wire is stretched by a force. The ratio of elongation in copper to steel is ($Y_{steel} = 2 \times 10^{11} \text{ Pa}, Y_{copper} = 1.1 \times 10^{11} \text{ Pa}$):

• A. 1.1 : 2
• B. 2 : 1.1
• C. 1 : 1
• D. 4 : 1.1

Hint:

For the same stress, the material with a lower Young's Modulus will elongate more.

Answer 1

The Correct Option is B

Step 1: Concept
Elongation $\Delta l = \frac{Fl}{AY}$.
Step 2: Analysis
Since $F, l,$ and $A$ are the same for both, $\Delta l \propto 1/Y$. $\frac{\Delta l_{cu}}{\Delta l_{s}} = \frac{Y_{s}}{Y_{cu}} = \frac{2 \times 10^{11}}{1.1 \times 10^{11}}$.
Step 3: Conclusion
The ratio is 2 : 1.1.
Final Answer: (B)