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Question:

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

Length=50 cm,diameter=0.5 mm

Length=100 cm,diameter=1 mm

Length=300 cm,diameter=3 mm

Length=200 cm,diameter=2 mm

Solution:

Using Hooke's law:
Y = FL/AΔL
where A = πD²/4
⇒ ΔL = KL/D²
where K = constant
For wire A: L/D² = 50/(0.05)² = 20000
For wire B: L/D² = 100/(0.1)² = 10000
For wire C: L/D² = 200/(0.2)² = 5000
For wire D: L/D² = 300/(0.3)² = 3333.33
Thus wire A has the largest extension.