Gravity is the law that if any 2 objects are floating & free of resistance they will be atracted to each other. I\'m not sure if the gravity is any stronger at the center of the earth, but the lack of centrifugal force is what makes it seem like there\'s more gravity. (I\'m not positive on any of this)
So I think the Metal Ball would go to the center and then stick to the side of the tube.