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A wire of length L and radius r, clamped at one end, stretches by l when pulled with force f at the other end. A second wire of the same material, of length 2L and radius 2r, is pulled by a force 2f. Find the increase in length of the second wire.

1. l/2
2. l
3. 2l
4. 4l

Correct answer: l

Solution

Elongation scales as F*L/r²; substituting F->2f, L->2L, r->2r gives a factor (2*2)/(4) = 1, so the elongation is l.

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