UPSC Prelims 2002 Q121: Science & Technology – Physics
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?
- (a) Circular plate
- (b) Cube
- (c) Sphere
- (d) All of them will reach the room temperature at the same time
Answer: (a) Circular plate
Explanation
Cooling of a hollow sphere, a hollow cube and a thin plate
| Body | Cooling feature |
|---|---|
| Thin circular plate | Thinnest, so the largest surface area for its mass; loses heat fastest |
| Hollow cube | Thicker shell, smaller area per unit mass |
| Hollow sphere | Smallest surface for its volume; loses heat slowest |
| Same time for all | Not true, since the area-to-mass ratio differs |
The three bodies are of the same material and are heated to 20 °C above the room temperature. The rate of loss of heat depends on the surface area exposed, and the thin circular plate has the greatest area for its mass. So the circular plate reaches room temperature first. The stored key (c), the sphere, is wrong, because the sphere has the least surface for its volume and cools slowest.
Answer: (a) Circular plate.
Why each option is right or wrong
- (a) CORRECT. The thin plate has the largest area per unit mass.
- (b) Incorrect. The cube has less surface per unit mass than the plate.
- (c) Incorrect. The stored key is wrong; the sphere has the least surface area per unit volume.
- (d) Incorrect. The bodies differ in surface area to mass ratio, so times differ.
Key point
Rate of cooling ∝ surface area exposed ÷ heat capacity; thin plates cool faster than compact shapes.
Remember
Largest area for its mass cools first.
Common mistakes
- Trusting the stored key and choosing the sphere.
- Assuming equal times because the material is the same.
- Ignoring the shape and thickness of each body.
Exam tip
Think of why a spread-out plate cools faster than a compact ball.
Sources
- NCERT Class XI Physics — Thermal Properties of Matter
- H. C. Verma — Concepts of Physics, Volume 2 (Heat Transfer)