Soldato
But the centre of mass isn't in the middle surely?
No, the centre of mass is definitely in the middle of a sphere. If you're standing say on the inside of the sphere on one point, then the majority of the mass of the body will be above you and you'll be attracted to that. The point where you'll be attracted by the whole body equally will be in the centre.
. I was of course naturally assuming Kwerk's room is nice and practical - i.e. has air in it (and a sofa, etc). In that case there is still a net force towards the centre. Only a true hollow shell (vacuum inside) would have zero net force everywhere inside.