TITLE: An example that a 2D shape with its centre of mass on its boundary
QUESTION [14 upvotes]: The object has constant density. Could any body suggest one for me?

REPLY [3 votes]: It's hard to improve on @YvesDaoust 's answer, but this athletic feat suggests another: in a well executed high jump, the jumper's center of gravity stays well under the bar, so is outside his (or her) body. At some point in the jump it's on his boundary.
Pictures here, including one that is a direct answer to the question:
http://nrich.maths.org/2742