Official Answer Key & Detailed Solution
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Official UPSC Answer KeyUPSC Prelims 2007 • Science and Technology
Correct Answer: Option (C) — Wire of 3 m length and 1.5 mm diameter
Concept & Option Breakdown
Standard Reference VerifiedElongation $\Delta L = \frac{F L}{A Y} = \frac{4 F L}{\pi d^2 Y}$. Since $F$ and $Y$ are identical for all wires, elongation is proportional to $\frac{L}{d^2}$:
- Option (a): $1 / 2^2 = 0.25$
- Option (b): $2 / 2^2 = 0.50$
- Option (c): $3 / (1.5)^2 = 3 / 2.25 = 1.33$
- Option (d): $1 / 1^2 = 1.00$ Wire with $L = 3\text{ m}$ and $d = 1.5\text{ mm}$ gives the highest ratio (1.33) and will elongate the maximum.
Elimination Heuristic & Exam Approach
Direct formula evaluation: Elongation $\propto L/d^2$. Maximize length and minimize diameter.
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