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A horizontal wire of cross-sectional area A is clamped at two fixed points that are 2l metres apart. A weight W is hung from the midpoint of the wire, causing the midpoint to sag a vertical distance x, where x << l. What is the longitudinal strain produced in the wire?
- 2x²/l²
- x²/l²
- x²/(2l²)
- none of these
Correct answer: x²/(2l²)
Solution
Each half of the wire stretches from l to sqrt(l²+x²) approximately l + x²/(2l). The total extension is x²/l and the original length is 2l, giving strain = x²/(2l²).
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