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

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$ℓ = 50 c m$ and diameter $0.5 m m$

$ℓ = 100 c m$ and diameter $1.0 m m$

$ℓ = 200 c m$ and diameter $2.0 m m$

$ℓ = 300 c m$ and diameter $3.0 m m$

answer is A.

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Detailed Solution

$e \propto \frac{1}{r^{2}}$

$ℓ$ should be more, r should be , Less to have more elongation

$e \propto \frac{l}{r^{2}} \propto \frac{50}{{(0.25)}^{2}} \propto 800$

$\Rightarrow e \propto \frac{l}{r^{2}} \propto \frac{100}{{(0.5)}^{2}} \propto 400$

$\Rightarrow e \propto \frac{l}{r^{2}} \propto \frac{200}{{(1)}^{2}} \propto 200$

$\Rightarrow e \propto \frac{l}{r^{2}} \propto \frac{300}{{(1.5)}^{2}} \propto 133.3$

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