I read in “N. David Mermin, It’s about time, (Princeton University Press, 2005) p.144:
”Furthermore, even when you put together identical bricks, it turns out (in the relativistic case) that the mass of the object you construct depends on how you put the bricks together.”
In order to test the way in which the students understand the statement I proposed them the following problem:
Consider a high sensitivity balance with equal arms. Put on its left pan a cube of volume a3. Put on its right pan a sphere of radius r made from the same material (density ). The balance is located in a uniform vertical gravitational field (g). The balance being in a state of mechanical equilibrium and in thermal equilibrium with the surrounding, determine the relationship between a and r.
what is the solution you propose?