Two wires of the same material carry the same load. How can I tell which stretches more?
Start from Delta L = FL/(AY).
Start from Delta L = FL/(AY). The material and load make Y and F the same, so extension is proportional to L/A. A longer wire stretches more; a thicker wire with larger cross-sectional area stretches less. Compare area, not radius directly: for a circular wire A is proportional to r squared, so doubling radius reduces extension to one-fourth.
Key point
For fixed material and load, extension is proportional to L/A.
Common mistake
assuming extension is inversely proportional to radius instead of radius squared.
Memory tip
long stretches; thick resists.
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