Supposing we have a uniformly mass distributed hemisphere of some radius, so what will be direction of gravitational field throughout the flat surface of hemisphere? And why?
In the flat, you will feel it falls down the mountain side to the center Due the direction of gravity would be at the center of mass.
A picture is worth a thousand words.
In a uniformly mass distributed hemisphere of radius r, the center of mass is given by geometric centroid. The geometric centroid of an heisphere is then given by
3/8 * r