Is a nucleus more dense than the rest of the cell?
When you hang up your shirt does it fall to the bottom of your closet?

The nucleus is a dense fibrillar network of DNA, RNA, and proteins, yes, but the subject you should take a look at is the cytoskeleton of the cell. It will will answer all your unanswered questions on the intracellular network that stabilizes, supports, and aligns the organelles within the cell.