(a) | the same stress | (b) | different stress |
(c) | the same strain | (d) | different strain |
1. | (a), (b) | 2. | (a), (d) |
3. | (b), (c) | 4. | (c), (d) |
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.
© 2024 GoodEd Technologies Pvt. Ltd.