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Question

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area $$A$$ and wire 2 has cross- sectional area $$3A$$. If the length of wire 1 increases by $$\Delta \mathrm{x}$$ on applying force $$\mathrm{F}$$, how much force is needed to stretch wire 2 by the same amount  ?


A
F
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B
4F
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C
6F
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D
9F
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Solution

The correct option is D $$9\mathrm{F}$$
$$\ell_{1}=3\ell_{2}$$ (given)
$$\displaystyle \mathrm{Y}=\frac{\mathrm{F}}{\mathrm{A}}\times\frac{\ell_{1}}{\Delta \mathrm{x}}$$ (i)             [symbols have their usual meaning]
$$\displaystyle \mathrm{Y}=\frac{\mathrm{F}^{1}}{3\mathrm{A}}\times\frac{\ell_{1}/3}{\Delta \mathrm{x}}$$ (ii)
$$\displaystyle \frac{\mathrm{F}}{\mathrm{A}}\times\frac{\ell_{1}}{\Delta \mathrm{x}}=\frac{\mathrm{F}'}{3\mathrm{A}}\times\frac{\ell_{1}}{3\Delta \mathrm{x}}$$
$$\mathrm{F'}=9\mathrm{F}$$

Physics

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