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Question

The ratio of lengths of two wires made of same material is $$2 :3$$. The ratio of their respective longitudinal stress to produce same elongation is


A
4:9
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B
9:4
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C
2:3
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D
3:2
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Solution

The correct option is D $$3: 2$$
$$\dfrac{L_{1}}{L_{2}}=\dfrac{2}{3}$$
$$\Delta L_{1}=\Delta L_{2}$$ (given)
$$y_{1}=y_{2}$$ (given)
$$\dfrac{\sigma _{1}}{\epsilon _{1}}=\dfrac{\sigma _{2}}{\epsilon _{2}}$$ (as inferred from question)
$$\dfrac{\sigma _{1}}{\sigma _{2}}=\dfrac{\epsilon _{1}}{\epsilon _{2}}$$
$$\dfrac{\sigma _{1}}{\sigma _{2}}=\dfrac{\Delta L_{1}}{L_{1}}\times \dfrac{L_{2}}{\Delta L_{2}}$$$$=\dfrac{3}{2}\times 1$$

Physics

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