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 \(1\) cm. The two wires will have:
(a) the same stress (b) different stress
(c) the same strain (d) different strain

Choose the correct option:
1. (a), (b) 2. (a), (d)
3. (b), (c) 4. (c), (d)
Hint: The tension or compression in the wires will be the same.
 

Step 1: Find the stress in both the wires.
Consider the diagram where a deforming force \(F\) is applied to the combination.
    
For steel wire, \(Y_\text{steel} = \frac{\text{Stress}}{\text{Strain}} = \frac{\frac{F}{A}}{\text{strain}_\text{steel}}\)
For copper wire, \(Y_\text{copper} = \frac{\text{Stress}}{\text{Strain}} = \frac{\frac{F}{A}}{\text{strain}_\text{copper}}\)
where \(F\) is tension in each wire and \(A\) is the cross-section area of each wire.
As \(F\) and \(A\) are the same for both the wires,
Therefore, stress will be the same for both the wires.

Step 2: Find the strain in the two wires.
The strain in the wire is given by; 
Strain = \(\frac{\text{Stress}}{Y}\)
\(\Rightarrow \text{Strain}_\text{steel} = \frac{\text{Stress}}{Y_\text{steel}}\)
\(\Rightarrow \text{Strain}_\text{copper} = \frac{\text{Stress}}{Y_\text{copper}}\)
As \(Y_\text{steel}\ne Y_\text{copper}\)
Therefore, the two wires will have different strains.
Hence, option (2) is the correct answer.