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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.

1. 0.25
2. 0.50
3. 2.00
4. 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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