(EFOMM 2026) Uma questão de Hidrostática que separa os homens dos meninos...

A solid cube is fixed at point A on the solid sphere of radius r in the figure. Both have a homogeneous mass distribution. The system floats in equilibrium in a fluid of density ρ_1, with only the volume of the spherical cap determined by the angle α=CB ̂D=120° exposed to the atmosphere. Then, the assembly is rotated 180° around the y-axis and placed in equilibrium in another fluid of density ρ_2, a situation in which the cube and the same spherical cap of angle α are now submerged. Mark the option that corresponds to the ratio ρ_2/ρ_1, knowing that the ratio between the volume of the cube and the volume of the sphere is 1/8, and that the volume of the spherical sector BCAD is 4/3 πr³sen²(α/4) Note: The spherical sector is obtained by rotating the circular sector ABC around the z-axis. #ita #ime #efomm