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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?

A
Length=50 cm,diameter=0.5 mm
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B
Length=100 cm,diameter=1 mm
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C
Length=200 cm,diameter=2 mm
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D
Length=300 cm,diameter=3 mm
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Solution

The correct option is B Length=50 cm,diameter=0.5 mm
Using Hook'e law Y=FLAΔL where A=πD24
ΔL=KLD2 where K=constant
For wire A : LD2=50(0.05)2=20000

For wire B : LD2=100(0.1)2=10000

For wire C : LD2=200(0.2)2=5000

For wire D : LD2=300(0.3)2=3333.33
Thus wire A has the largest extension.

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