What can be said about the centre of mass of a solid hemisphere of radius `r` without making any calculation. Will its distance from the centre be more than `r//2` or less than `r//2`?

Explanation

To determine the position of the center of mass of a solid hemisphere of radius \( r \) without performing any calculations, we can analyze the distribution of mass within the hemisphere.

### Step-by-Step Solution:

1. **Visualize the Hemisphere**:
- Consider a solid hemisphere placed on a flat surface. The flat circular face is at the bottom, and the curved surface is on top.

2. **Understand the Mass Distribution**:
- The hemisphere can be divided into two regions: the upper half (the curved part) and the lower half (the flat circular base).
- The mass distribution is not uniform; more mass is concentrated in the upper part of the hemisphere compared to the lower flat circular base.

3. **Identify the Center of Mass**:
- The center of mass of an object is the point where the mass is evenly distributed in all directions.
- In the case of the hemisphere, since the upper region has more mass, the center of mass will be located closer to this region.

4. **Compare Distances**:
- The center of mass will be at a distance from the flat circular base. Since the upper region has more mass, the center of mass will be located above the midpoint of the radius.
- The midpoint of the radius is at \( \frac{r}{2} \). However, because the upper part has more mass, the center of mass will be positioned at a distance less than \( \frac{r}{2} \) from the flat base.

5. **Conclusion**:
- Therefore, we can conclude that the distance of the center of mass of the solid hemisphere from the center (the flat circular face) is less than \( \frac{r}{2} \).

### Final Answer:
The distance from the center of a solid hemisphere to its center of mass is less than \( \frac{r}{2} \).