1. The problem statement, all variables and given/known data An empty cylindrical beaker of mass 100g, radius 30mm and negligible wall thickness, has its centre of gravity 100mm above its base. To what depth should it be filled with water so as to make it as stable as possible? Spoiler 55.9mm 2. Relevant equations Center of mass equations 3. The attempt at a solution I tried to find the point which the beaker's center of mass gets furthest from the vertical by rotating the base, while in equilibrium, but the problem is to find the distance of the water's center of gravity to the vertical. How should I get it? Besides, I've found a solution which says: "Clearly, for maximum stability the overall centre of gravity must lie in the water surface". It's correct, but how can I prove it?