# Can two objects be considered physically identical, given that their shape, mass, and center of mass are the same?

I came up with a problem, which is to find a way to measure the mass of a 'certain part' of a stick without breaking it.

For instance, given a stick 10cm long, I want to know how to find out the mass of the stick between x=0 and x=5.

The density might not be uniform, so the answer isn't simply half the total mass.

I couldn't find a way, and am guessing that such a method doesn't exist.

If gravity can be completely simplified as a sigle pull on the center of mass, it would mean that two objects with the same mass, shape, and center of mass would be 'physically identical', thus leading to the conclusion that finding a solution to the problem is impossible.

(It is possible for two objects to have a different density distribution and still have the center of mass at the same position, so we won't be able to tell them apart)

However, that such a simple task would be impossible seemed too bizarre, and I suspected that there would be a slight difference between two objects mentioned above. Is there a difference?

Conditions are: The stick is in a uniform gravity field, and density does not affect anything other than the gravital pull.