The following four wires of length L and radius r are made of the same material.Which of these will have the largest extension, when the same tension is applied ?

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L=100cm, r=0.2mm

L=400cm, r=0.8mm

L=200cm, r=0.4mm

L=300cm, r=0.6mm

answer is A.

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Detailed Solution

Extension of wire $e = \frac{F L}{A Y} \Rightarrow e = \frac{F L}{π r^{2} Y}$
Since, F and Y are same for all wires

$\begin{array}{l} ∴ e α \frac{L}{r^{2}} \\ e_{a} = \frac{100}{0.2 \times 0.2} = 2500 e_{b} = \frac{200}{0.4 \times 0.4} = 1250 \\ e_{c} = \frac{300}{0.6 \times 0.6} = 833.4 \\ e_{d} = \frac{400}{0.8 \times 0.8} = 625 \end{array}$

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