Official Answer Key & Detailed Solution
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Official UPSC Answer KeyUPSC Prelims 2002 • Science and Technology
Correct Answer: Option (C) — Sphere
Concept & Option Breakdown
Standard Reference VerifiedAccording to Stefan-Boltzmann's law and Newton's law of cooling, rate of heat radiation is directly proportional to surface area ($A$). For hollow shapes of negligible wall thickness:
- Sphere surface area $= 4\pi R^2 \approx 12.57 R^2$
- Cube surface area $= 6 R^2$
- Circular plate surface area (both faces) $= 2\pi R^2 \approx 6.28 R^2$ The hollow sphere has the largest total radiating surface area among the given shapes of dimension $R$, dissipating heat to the surroundings fastest and thus reaching room temperature first.
Elimination Heuristic & Exam Approach
For fixed characteristic dimension $R$, compare surface areas: $4\pi R^2 > 6R^2 > 2\pi R^2$. Maximum surface area leads to fastest cooling.
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