Two spheres A and B are made of the same material and have...

Two spheres $A$ and $B$ are made of the same material and have the same radius. Sphere $A$ is hollow and sphere $B$ is solid. Both the spheres are heated to the same temperature. Which of the following is correct? (a) A expands more than $B$. (b) A expands less than $B$. (c) Both the spheres expand equally. (d) Data is insufficient.

Two spheres $A$ and $B$ are made of the same material and have the same radius. Sphere $A$ is hollow and sphere $B$ is solid. Both the spheres are heated to the same temperature. Which of the following is correct?
(a) A expands more than $B$.
(b) A expands less than $B$.
(c) Both the spheres expand equally.
(d) Data is insufficient.

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Key Concepts

Influence of Geometry on Expansion

In thermal expansion, the rate of change of the external dimensions is primarily dictated by the material’s properties rather than by its internal structure or whether it is hollow or solid. Thus, for objects with the same external dimensions and made from the same material, the thermal expansion behavior will be analogous even if their internal compositions differ.

Coefficient of Thermal Expansion

The coefficient of thermal expansion is an intrinsic property of a material that quantifies the relative change in size per degree change in temperature. Since this coefficient is determined by the material itself, objects made of the same material will expand similarly when subjected to the same temperature change regardless of their internal structure, as long as the measurements refer to the same dimensions.

Thermal Expansion

Thermal expansion is the phenomenon where materials increase in size due to a rise in temperature. When an object is heated, its particles vibrate more vigorously, leading to an increase in the average distance between them. This results in an expansion of the object’s dimensions, which is characterized by specific expansion coefficients for materials.

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