UPSC Prelims 2002 · General Studies
Question 121: Science and Technology
A hollow sphere of radius R, a hollow cube of side R and a thin circular plate of radius R, made up of the same material, are all heated to 20 °C above room temperature. When left to cool in the room, which of them will reach the room temperature first?
AnswerThe answer is (c).
Heat is lost through the surface, and the given answer reasons that the body with the largest exposed surface area cools fastest. With the same R, the hollow sphere has an area of 4 pi R-squared, about 12.6 R-squared; the hollow cube has 6 R-squared; and the thin circular plate, counting both faces, has 2 pi R-squared, about 6.3 R-squared. The sphere has the greatest surface area, so it is taken to reach room temperature first.
Why each option is right or wrong
- (a) The thin plate has the smallest area here, about 6.3 R-squared, so by this reasoning it is slowest.
- (b) The cube has 6 R-squared of surface, less than the sphere.
- (c) Right as given: the sphere has the largest surface area.
- (d) The three differ in surface area, so the times are not equal.
Worth knowing: The question gives no wall thickness or mass, which also affect cooling time, so the key's reasoning from surface area alone is open to challenge.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2002, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.