Question

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of $200^\circ$C. On these are left in a room.

• A. the sphere reaches room temperature fast
• B. the cube reaches room temperature fast
• C. the circular plate reaches room temperature fast
• D. all will reach the room temperature simultaneously

Hint:

Physics Tip : For same volume, sphere has minimum surface area.

Answer 1

The Correct Option is C

Step 1: Same material and same mass. Since all three bodies are made of same material and have same mass:
• Density is same
• Heat capacity per unit mass is same
• Total heat to be lost for same temperature fall is same So cooling rate mainly depends on exposed surface area.

Step 2: Law of cooling / radiation idea. Rate of heat loss is proportional to surface area: $$ \frac{dQ}{dt}\propto A $$ Larger surface area means faster transfer of heat to surroundings.

Step 3: Compare shapes. For same mass (hence same volume approximately):
• Sphere has minimum surface area.
• Cube has more surface area than sphere.
• Thin circular plate has maximum exposed area.

Step 4: Cooling consequence. Since thin circular plate has largest area, it loses heat fastest and reaches room temperature first.

Step 5: Conclusion. $$ \therefore \text{Correct option is (C).} $$