Question

Two spheres $A$ and $B$ are made of the same material and have the same radius. Sphere $A$ is hollow and sphere $B$ is a solid. Both the spheres are heated to the same temperature. Which of the following is correct?
A) $\text{A expands more than B}$.
B) $\text{A expand less than B}$.
C) $\text{Both the spheres expand equally}$.
D) $\text{Data is insufficient}$.

Answer 1

Hint: The thermal expansion is the increase in the size, shape, area, volume and the density of the object but it does not include the changes in the phase transition of the liquid like solid to liquid, or liquid to the gas. This is because the increase in the temperature causes the function of the kinetic energy of the object.

Complete step by step solution:
It is given that the both the spheres $A$ and $B$ are made by using the same material. The only difference between the material is, the sphere $A$ is hollow in nature and the sphere $B$ is solid in nature. It is known that at the time of heating and when the temperature is increased, all the materials get expanded to some proportion. The expansion of the object depends upon the material that makes up an object. Hence in this case, even though some amount of the material is lost in the centre of the sphere in the hollow sphere, it also expands in the same manner as the solid sphere expands since they are made up of the same material and the same radius.

Thus the option (C) is correct.

Note: The example of the thermal expansion is the tightening of the doors in the summer than in the winter. The electrical cables lines found sagging during the temperature due to the expansion of the cable lines and it remains tight during the winter.