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  • A wire of length  and radius <img alt="1 \mathrm{~mm}" src="https://entrancecorner

A wire of length 1 \mathrm{~m} and radius 1 \mathrm{~mm} is subjected to a load. The extension is 'x'. The wire is melted and then drawn into a wire of square cross-section of side 1 \mathrm{~mm}. What is the extension under the same load?

Option: 1

\frac{\pi^2}{x}


Option: 2

\pi x^2


Option: 3

\pi^2 x


Option: 4

\pi x


Answers (1)

best_answer

\pi(1)^2 \times 1=1^2 \times l \Rightarrow l=\pi

Using, \Delta l=\frac{F l}{A Y}
\begin{aligned} & \frac{\Delta l_1}{\Delta l_2}=\frac{l_1}{l_2} \times \frac{A_2}{A_1}=\frac{1}{\pi} \times \frac{1^2}{\pi(1)^2} \\ & \Delta l_2=\pi^2\left(\Delta l_1\right)=\pi^2 x \end{aligned}
 

Posted by

seema garhwal

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