I think your assumptions are unrealistic. A fiber optic cable weighing 4kg per km with no other reinforcement or protection would be extremely fragile.
According to my back-of-the-envelope math, using the density and tensile strength of typical glass, it would have a breaking load capacity of around 10 newtons (roughly 2 pounds of force). Even a steel cable with the same weight would only be about 20 times stronger.
4kg/km it's not for clean glass fiber. it's fiber drop cable, in whatever plastic sleeving + a couple of steel strands for some added rigidity/structure.
there are also versions with kevlar braiding to protect core and improve resilience.
According to my back-of-the-envelope math, using the density and tensile strength of typical glass, it would have a breaking load capacity of around 10 newtons (roughly 2 pounds of force). Even a steel cable with the same weight would only be about 20 times stronger.