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The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum for the same applied force?

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l = 200 cm and diameter 2 mm

l = 100 cm and diameter 1 mm

l = 50 cm and diameter 0.5 mm

l = 300 cm and diameter 3 mm

answer is D.

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Detailed Solution

$e α \frac{l}{r^{2}}$

$e_{1} α \frac{100}{{(\frac{1}{2})}^{2}} \propto 400$

$e_{2} α \frac{200}{{(1)}^{2}} \propto 200$

$e_{3} α \frac{300}{{(1.5)}^{2}} \propto 133.3$

$e_{4} α \frac{50}{{(0.25)}^{2}} \propto 800$

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