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A uniform circular cylinder of mass M and radius a lies at rest inside a fixed hollow cylinder of radius 3a.

A uniform circular cylinder of mass M and radius a lies at rest inside a fixed hollow cylinder of radius 3a. The axes of both cylinders are horizontal. A particle of mass m is fixed to a point at the top of the inner cylinder which can roll without slipping inside the hollow cylinder. The system is subject to a vertical gravitational field g.

as shown in the diagram.
ii) Find an expression for the gravitational potential energy of the system as a function of .
iii) Locate the positions of equilibrium and determine the relationship between M and m for the initial position to be one of stable equilibrium. Show that in this case it is the only equilibrium position.

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