unless you have an uneven weight distribution within the teardrop you can set it on its side no? The condition here is that the volume has an even mass distribu

unless you have an uneven weight distribution within the teardrop you can set it on its side no? The condition here is that the volume has an even mass distribution. Even if the teardrop resists being placed on its side, it seems to me that at some point along the side you must have a ring beyond which it falls the other way. The boundary would therefore consist of a ring of many unstable points