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Two metallic wires P and Q are made of the same material and have the same volume. Their cross-sectional areas are in the ratio 2:1. If the forces required to produce the same extension in both wires are F1 (for P) and F2 (for Q) respectively, find the ratio F1/F2.
- 4
- 8
- 16
- 32
Correct answer: 4
Solution
Both wires have same volume V, so L = V/A. Extension: delta_L = F*L/(A*Y) = F*V/(A²*Y). For same extension and same Y, V: F proportional to A². F1/F2 = A_P²/A_Q² = (2)²/(1)² = 4.
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