The following four wires are made of the same material.

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

1. Length = 100 cm, diameter = 1 mm
2. Length = 200 cm, diameter = 2 mm
3. Length = 300 cm, diameter = 3 mm
4. Length = 50 cm, diameter = 0.5 mm

Correct Option: D

F = YA/L × l So, extension, l ∝ L/A ∝ L/D² [∵ F and Y are constant]
l₁ ∝ 100/l² ∝ 100 and l₂α (200/2²)∝ 50
l₃∝ 300/3² ∝ 100/3 and l₄ ∝ (50/(1/4)) ∝ 200
The ratio of L/D² is maximum for case (d).
Hence, option (d) is correct.