This is amusingly similar to the old chestnut "I have a rope of nonuniform thickness, and it will take one hour to burn its entire length. How can I measure half an hour?"
https://en.m.wikipedia.org/wiki/1954_Guatemalan_coup_d'%C3%A...
https://www.exploratorium.edu/snacks/center-gravity
> Here’s an easy way to find the center of gravity of a long, thin object, even if the object’s weight is unevenly distributed.