Question
A metal disc with a hole in the middle is heated. Does the hole get bigger or smaller? Many students answer “smaller” because the metal expands inward. Why is that wrong?
Solution — Step by Step
When a body heats up uniformly, every linear dimension scales by the factor . Imagine taking a photo and enlarging it — every distance, including the hole’s diameter, scales up.
The hole’s diameter is just the distance between two points on the metal disc. Both points expand outward as the metal heats. So the hole’s diameter scales up by the same factor as the disc itself.
The hole expands as if it were filled with the same metal — even though it is empty.
If the original hole diameter is , the new diameter is:
For steel () heated by , the diameter grows by . Small but measurable.
The hole gets bigger when the disc is heated.
Why This Works
The key insight: thermal expansion is a uniform scaling. Every linear dimension grows in the same ratio. Holes, gaps, and cavities scale up exactly like the surrounding solid material.
This is why a lid that is stuck on a glass jar comes off easily after we run hot water over it — both the lid and its hole expand, but the metal lid expands MORE than the glass (steel’s is about 4× glass’s), so the hole in the lid grows faster than the glass jar’s neck.
Alternative Method — Visualise with a Solid Disc
Imagine the disc was solid (no hole). Heat it. It expands uniformly — every atom moves outward. Now mentally remove the central region. The cavity left behind has the new, larger size.
This thought experiment proves the hole must grow — there is no way for it to shrink while the surrounding material expands outward.
Memory hook: “Holes expand like solids.” Whenever a question involves heating an object with cavities, treat the cavities as if they were filled with the same material. Same expansion coefficient, same scaling factor.
Common Mistake
Students often visualise the metal “pushing inward” as it expands, shrinking the hole. This is wrong — atoms maintain their relative positions and just spread further apart, so the geometry scales up uniformly.
Another classic trap: thinking that bimetallic strips work because one metal’s hole shrinks while the other’s hole grows. Actually both metals expand outward — they bend because their expansion coefficients differ.
JEE Main 2019 asked about the area of a hole in a heated steel plate. The answer uses superficial expansion: . Same scaling rule, just with instead of because area is two-dimensional. NEET asks similar concepts via “ring on rod” problems.