Create a FBD for segment 2 that is attached to the lower end of the cord. Assume, for the moment, that the weight is in equilibrium.  Given:  Enumerate the segments as i=1,⋯,N from the lower to the upper end.   Let T0 be the tension at the lower end of the cord.   Let Ti be the tension at the upper end of segment i.

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Center of Gravity of a system

The centre of gravity is a property that is based on the geometry of a rigid body or any particle. It is described as an equilibrium point or a hypothetical location where the total weight of the body is concentrated.