Cube with water · Estonian PhO 2018 #7

Physics · fluid-mechanics

Problem

Find the mass of the water that has to be poured into a cube so that the cube would be as stable as possible, meaning that the system’s center of mass would be as low as possible. The length of the cube’s edge is aa, the mass MM, density of water ρ\rho. Do not consider the width of the cube’s wall. The cube is completely symmetrical meaning that it has all 6 identical faces.

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