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Two wires A and B are made of the same material and have the same initial length. Their radii are in the ratio 1:2. If both wires are stretched by identical loads and the extension of wire A is 8 mm, what is the extension of wire B?

1. 2 mm
2. 4 mm
3. 8 mm
4. 16 mm

Correct answer: 2 mm

Solution

Same material/length/load: e = FL/(A*Y) and A ~ r^2, so e ~ 1/r^2. B has twice the radius, hence 4x the area, so e_B = e_A/4 = 8/4 = 2 mm.

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