Would a square table placed at its perfect centre on a football on a flat surface topple over?

Answer 1

If everything was perfectly centred, smooth, round etc then yes it should balance - but the equilibrium would be very unstable - the slightest movement would send the system toppling.

Answer 2

How big is the table? Is the table upside-down? Is the football inflated? Assuming that the table is upside-down and considerably larger than the football, i would say yes, it will topple because the area of the football that would support the table is going to be uneven.
Of course, I'm also assuming that the football is of the American variety, but your spelling of the word "centre" makes me wonder if you're referring to what I might call a soccer ball?

Answer 3

Not to be egotistical, but a general discussion and semi-solution to the problem of stability of a rectangular solid balanced on a hemisphere is pretty well covered in the ref. including followup comments. The football doesn't exactly fit since its surface has major and minor radii, but the general idea is that if the CM of the solid is less than 1 radius above the ball's surface there is a region of stability, which grows as the CM height decreases.

Answer 4

If the floor is perfectly horizontal,
If the point of contact bet. the floor & the lower side of the football, the centre of gravity of the football,& the point of contact bet, the ball and the table are in the same , perfect vertical line,
If the centre f gravity of the table lies in the above vertical line,
If there is no wind,
If there is no tremour on the floor,
the "System" is supposed to be balanced.

Answer 5

If everything was balanced perfectly and there was no breeze then it should balance fine.

Answer 6

only if you sat on it ;-)