(Solution) - Two small spheres of mass m are suspended -(2025 Original AI-Free Solution)

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Two small spheres of mass m are suspended from strings of length ? that are connected at a common point. One sphere has charge Q; the other has charge 2Q. The strings make angles ?1 and ?2 with the vertical.
(a) How are ?1 and ?2 related?
(b) Assume ?1 and ?2 are small. Show that the distance r between the spheres is given by