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A wire of length $1 m$ and radius $1 m m$ is subjected to a load. The extension is $' x'$ . The wire is melted and then draw into a wire of square cross-section of side $1 m m$ . What is its extension under the same load

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$π^{2} x$

$π x^{2}$

$π x$

$π / x$

answer is A.

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Detailed Solution

Volume = const $V_{1} = V_{2}$

$A_{1} ℓ_{1} = A_{2} ℓ_{2} \Rightarrow \frac{ℓ_{1}}{ℓ_{2}} = \frac{A_{2}}{A_{1}}$

$e = \frac{F ℓ}{A Y}$ as $F & Y$ $\to$ same

$e α \frac{ℓ}{A} \Rightarrow \frac{e_{1}}{e_{2}} = \frac{ℓ_{1}}{ℓ_{2}} . \frac{A_{2}}{A_{1}}$ $= (\frac{A_{2}}{A_{1}}) (\frac{A_{2}}{A_{1}})$

$\frac{x}{e_{2}} = {(\frac{A_{2}}{A_{1}})}^{2} = {(\frac{10^{- 6}}{π \times 10^{- 6}})}^{2}$

$e_{2} = π^{2} x$

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