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Four wires of same material are stretched by the same amount of load. The dimensions are given below. Which of them will elongate the most?

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l = 300 cm, r = 3 mm

l = 200 cm, r = 3 mm

l = 50 cm, r = 0.5 mm

l = 100 cm, r = 1 mm

answer is D.

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Detailed Solution

$Y = \frac{FL}{Ae} = \frac{FL}{{πr}^{2} e} \Rightarrow e \propto \frac{L}{r^{2}}$

$\Rightarrow e_{1} \propto \frac{100}{1^{2}} \Rightarrow e_{1} \propto = 100$

$\Rightarrow e_{2} \propto \frac{200}{3^{2}} \Rightarrow e_{2} \propto \frac{100}{4.5}$

$\Rightarrow e_{3} \propto \frac{300}{3^{2}} \Rightarrow e_{3} \propto \frac{100}{3}$

$\Rightarrow e_{2} \propto \frac{50}{0 . 5^{2}} \Rightarrow e_{2} \propto 200$

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