Question

Let H be a solid hemisphere of radius ( a ) whose density at any point is proportional to its distance from the center of the base located at the origin.

Answer 1

The center of mass of a solid hemisphere with increasing density is not located at the geometrical center. Integration of the mass distribution can be used to find the center of mass.

Step-by-step explanation:

The center of mass of a solid hemisphere with increasing density is not located at the geometrical center. Instead, it is shifted towards the denser side. In this case, the density is proportional to the distance from the center of the base, which means the density increases as you move towards the curved surface of the hemisphere.

To find the center of mass, we can consider the missing part of the hemisphere as a negative mass overlapping a positive mass. By integrating the mass distribution, we can determine the location of the center of mass.