When a metal sheet is heated, it undergoes thermal expansion, which affects not just the material itself but also any holes or openings within it. Let's break down what happens to the holes of unequal diameters, d1 and d2, when the sheet is heated.

Understanding Thermal Expansion

Thermal expansion is a physical property of materials where they expand when heated and contract when cooled. This phenomenon occurs because the atoms in the material move more vigorously as temperature increases, leading to an increase in the average distance between them.

Effects on the Holes

In the case of the two holes, d1 (the larger hole) and d2 (the smaller hole), both holes are part of the same metal sheet. When the sheet is heated:

• The entire sheet expands, including the material surrounding the holes.
• As the surrounding material expands, the holes themselves also expand.

Therefore, the correct answer to the first question is (b) both d1 and d2 will increase. This is because the expansion of the metal sheet causes the holes to grow larger rather than smaller.

Considering the Distance Between the Holes

Now, let’s address the second question regarding the distance between the two holes after heating. Since both holes are expanding, we need to consider how their positions relative to each other change.

• If the holes are close together, the expansion of the material between them will also contribute to the distance.
• The distance between the holes will depend on the ratio of their diameters and their positions on the sheet.

As a result, the distance between the holes may either increase or decrease depending on how the expansion of the surrounding material affects their relative positions. Thus, the answer to the second question is (d) may either increase or decrease depending on the positions of the holes on the sheet and on the ratio d1/d2.

Real-World Analogy

Think of this situation like two balloons tied together with a string. If you blow up both balloons, they will expand, and the distance between them will change based on how they are positioned and how much each balloon expands. Similarly, the holes in the metal sheet behave like those balloons, expanding outward and affecting the distance between them based on their sizes and positions.

In summary, when a metal sheet is heated, both holes will increase in size, and the distance between them can vary based on their initial positions and sizes. This understanding of thermal expansion is crucial in fields like engineering and manufacturing, where precise measurements are essential.