When a thin metallic plate with a hole is heated, how does the area of the hole change?

• A. Increases at twice the rate the area of the metal increases
• B. Increases at the same rate as the area of the metal increases
• C. Decreases at twice the rate the area of the metal increases
• D. Decreases at the same rate as the area of the metal increases

Answer: (B)

When a thin metallic plate with a hole is heated, the dimensions of the plate, including the hole, will expand due to thermal expansion. The key principle at play here is that both the material surrounding the hole and the hole itself will expand as the temperature increases.

As the temperature rises, the atoms in the metal vibrate more, leading to an increase in the distance between them. This uniformly affects the entire structure of the plate. The area of the metal around the hole increases as the plate expands, and at the same time, the hole itself will not shrink but rather increase in size as the surrounding material moves outward.

The increase in the hole's area happens at the same rate as the increase in the area of the plate because both are subjected to the same thermal expansion effects. Therefore, if you analyze their rates of expansion, you will find that the hole expands in sync with the overall area of the metal. This characteristic of uniform expansion in all dimensions is a direct result of the physics of thermal expansion, reinforcing why the area of the hole increases at the same rate as the area of the metal.