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Question

A wire whose cross-section area is $$4 {mm}^{2}$$ is stretched by $$0.1 mm$$ by a certain weight. How far will a wire of the same material and length stretch, if its cross-sectional area is $$8 {mm}^{2}$$ and the same weight is attached?


A
0.5mm
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B
1.0mm
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C
0.05mm
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D
0.06mm
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Solution

The correct option is C $$0.05 mm$$
Young's modulus is given by:
$$Y = \cfrac{FL}{A\Delta L}$$

It remains the same for both cases as it is a property of the material.
$$\cfrac{FL}{A_1 \Delta L_1} = \cfrac{FL}{A_2 \Delta L_2}$$
$$\Delta L_2 = \cfrac{4}{8} \times 0.1 = 0.05\ mm$$

Physics

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