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  • The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied to each?Option: 1</strong

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied to each?

Option: 1

\mathrm{\text { length }=0.5 \mathrm{~m} \text {, diameter }=0.5 \mathrm{~mm}}


Option: 2

\mathrm{\text { length }=1.0 \mathrm{~m} \text {, diameter }=1.0 \mathrm{~mm}}


Option: 3

\mathrm{\text { length }=2.0 \mathrm{~m} \text {, diameter }=2.0 \mathrm{~mm}}


Option: 4

\mathrm{\text { length }=3.0 \mathrm{~m} \text {, diameter }=3.0 \mathrm{~mm}}


Answers (1)

best_answer

We know that
or    \mathrm{ \begin{aligned} F & =\frac{Y A l}{L}=\frac{Y l \pi r^2}{L} \\\\ l & =\frac{F L}{\pi r^2 Y} \end{aligned} }
Since Y and F are the same for all wires,\mathrm{ l \propto \frac{L}{r^2}} or l \mathrm{ \propto \frac{L}{d^2}}. It is easy to see that \mathrm{\frac{L}{d^2}} is the highest for the first wire. Hence the correct choice is (a).

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mansi

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