The following four wires are made of the same material. Which of these will have

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

Options

(a) length = 100 cm, diameter = 1 mm
(b) length = 200 cm, diameter = 2 mm
(c) length = 300 cm, diameter = 3 mm
(d) length = 50 cm, diameter = 0.5 mm

Correct Answer:

length = 50 cm, diameter = 0.5 mm

Explanation:

F = YA / L x l
So, extension l ∞ L / A ∞ L / D² [F and Y are constant]
l₁ ∞ 100 / 1² ∞ 100 l₂ ∞ 200 / 2² ∞ 50
l₃ ∞ 300 / 3² ∞ 100 / 3 l₄ ∞ 50 / 1 / 4 ∞ 200
The ratio of L / D² is maximum for case (d).

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