Ah! That ties everything together in a very direct, concrete way. I did briefly think of applying calculus but thought it would result in a mass-less container of water (and what other effects that might have on other physics assumptions) as the container height went to zero. Should have stuck...
:doh:, I now see where my blind spots were/are. Due to the wording of the question I was focused on 'mgh' as stand-in for E_g and was zeroed-in on fractional amounts of that. Instead this problem is really a question about center of mass and how that affects calculations of height for an object...
@BvU, Doc Al - Thanks for the welcome and response. I do understand that approach to getting the answer but if I apply that to individual blocks of water I do not get the same answer.
Some numbers:
1. Let 'h' = 6
2. Divide container 'X' and 'Y' into 6 individual containers of water (c1, c2...
The image doesn't seem to be appearing in the problem statement so here it is:
I already know the correct answer and the method to arrive at it. However, I didn't find it very satisfying. So in attempting to create an answer that was, imo, more intuitively satisfying I:
a. treated the...