I have an interesting question, that I've been struggling with for a while now, but I'm somehow messing it up. I haven't found anything on the internet (hard to search for something like this)(adsbygoogle = window.adsbygoogle || []).push({});

so I'm wondering if any of you know something useful about it, or do better at finding the solution. :)

Let's assume a container with a mass of M. This container has a base area of A, a height of h. It is a right prism/ or cylinder. (We consider the width of the walls of this container negligible).

We fill with this container with a fluid to the height of h_{f}. (it could be something else too, but I think of fluids as it is a question that arose during drinking some refreshments :) ) The density of the fluid/substance is d (or rho, but that doesn't show up correctly on my screen...)

The question is at what height of filling the container will the (common) center of gravity be the lowest for these, and where is that minimum point?

In real life: Imagine the following scenario: You've got a glass of water. When it's completely full, its center of gravity is at ~h/2, because vertically it's sort of/approximately "homogeneous". As you start drinking from it, the center of gravity goes down with the water level. But at some point it reaches a minimum and starts going back up, because the water's weight gets more and more negligible compared to the glass. Until finally when you empty the glass, the center of gravity returns to that approximately ~h/2.

So where's that water level and the center of mass belonging to it? :)

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# Lowest center of mass of a container + fluid

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