Think I have a glimmering of understanding now. If someone is riding a bicycle, the point of contact will always be directly below the centre of the wheel. Will think about that.
Mark 44: The smaller hemisphere is not really relevant.
Could you explain why the centre of the hemisphere will always be directly above the point of contact as long as the plane surface is horizontal.
I don't know why X is below C. It could have something to do with moments. Maybe if X is not vertically below C there will be a moment about some point.
A solid hemisphere has another, smaller solid hemisphere attached to each other at their plane, circular faces, so that the centre C of the circular bases of either coincide. A particle P is then attached to the edge of the plane circular face of the larger hemisphere. The composite object is...