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).