You ask WHAT it is, not where. I simply answer your question:
The centre of mass of any object is the point at which, for many calculation purposes, including for example balancing, inertia, and gravitational attraction, the total mass of the object may be regarded as being concentrated.
Do you mean a solid hemisphere or a hemispheric shell?
If solid, the center of mass lies 3/8 of the way along the particular radius that is normal to the flat face.
You can find many derivations of this, online.
The center of mass of a hemispheric shell is obviously going to be farther from the flat face;
and (counterintuitively?) turns out to be halfway along the radius. The reason is deeply related to the fact that the surface area of each spherical cap is 2 pi R h, where h is the distance from the "pole" to the center of the circle that cuts off the cap.
You should give a little detail as to what radius and which direction. Assuming a 1-unit and above x-y plane, the the center of mass of the hemisphere is (0, 0, 0.5).
it depends on mass distribution. if it is uniform mass distribution, it's (3/8)r
http://answers.yahoo.com/question/index?...
If it was solid, as I expect, then open up this link :
http://wiki.answers.com/Q/Where_the_cent...
general mathematics
