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A thick horizontal copper wire of length 2L and radius 2R is welded end-to-end to a thin copper wire of length L and radius R. The combination is stretched by forces applied at the two ends. Find the ratio of the elongation of the thin wire to that of the thick wire.
- 0.25
- 0.50
- 2.00
- 4.00
Correct answer: 2.00
Solution
With equal tension, elongation is proportional to L/r²; the ratio thin/thick = (L/R²)/(2L/(2R)²) = 2.00.
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