Two spheres A and B are made of the same material and have the same radius. Sphere A is hollow alnd 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

Options

A. A expands more than B.
B. A expands less than B.
C. Both the spheres expand equally.
D. Data is insufficient

Explanation

To solve the problem, we need to analyze the expansion of the two spheres, A and B, under the same temperature increase.

### Step-by-Step Solution:

1. **Understanding the Spheres**:
- Sphere A is hollow, meaning it has a cavity inside.
- Sphere B is solid, meaning it is completely filled with material.

2. **Material Properties**:
- Both spheres are made from the same material, which means they have the same coefficient of linear expansion.

3. **Effect of Heating**:
- When both spheres are heated to the same temperature, the material of both spheres will expand due to thermal expansion.

4. **Expansion of Hollow vs. Solid**:
- For a solid sphere (Sphere B), the entire volume expands uniformly.
- For a hollow sphere (Sphere A), the cavity inside will also expand. The material surrounding the cavity will expand outward, and the cavity will expand as if it were filled with the same material.

5. **Comparing Expansions**:
- The expansion of the hollow sphere (A) will be the same as if it were filled with the same material. This means that the hollow sphere will expand in a manner similar to the solid sphere.
- Therefore, both spheres will experience the same amount of expansion when heated to the same temperature.

6. **Conclusion**:
- Since both spheres expand equally due to the same material properties and the same temperature change, the correct answer is:
- **Option C: Both the spheres expand equally.**