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A steel wire of length 4.5 m and a copper wire of length 3.5 m are each stretched by the same amount when the same load is applied. The Young's modulus of steel to that of copper is in the ratio 12:7. What is the ratio of the cross-sectional area of the steel wire to that of the copper wire?

1. 3:4
2. 4:3
3. 9:7
4. 7:9

Correct answer: 3:4

Solution

Since the load (F) and the extension (delta L) are the same for both wires, A*Y/L must be the same for both. Hence A_steel/A_copper = (L_steel/L_copper)*(Y_copper/Y_steel) = (4.5/3.5)*(7/12) = 3/4.

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