We need to calculate the buoyance force on a partially immersed sphere. (a) Derive an expression for the buoyance force acting on a sphere as a function of the depth of immersion. (b) Plot this relation in non-dimensional form where the abscissa is the non- dimensional value of immersion depth (ratio of depth of immersion to the sphere diameter) and the ordinate is the non-dimensional buoyancy force (ratio of actual buoyancy force to the maximum buoyancy force). (c) In the plot in (b) above, what are the maximum and minimum values of the slopes? (d) In the plot in (b) above, identify the abscissa values that correspond to the minimum and maximum values of the slopes in the plot.

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