(Solution) - Each of the following planar objects is placed as shown -(2025 Original AI-Free Solution)

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Each of the following planar objects is placed, as shown in Fig. between two frictionless circles of radius R. The mass density of each object is Ï?, and the radii to the points of contact make an angle θ with the horizontal. For each case, find the horizontal force that must be applied to the circles to keep them together. For what θ is this force maximum or minimum?
(a) An isosceles triangle with common side length L.
(b) A rectangle with height L.
(c) A circle.