How to calculate the length of the cable at which it will break from its own weight?

Question

Mathematics

Steel cable, ~10 mm. Its mass is ~450kg per 1km

Answer 1

Obviously, to solve it, you also need to know the breaking force of the cable.
For a cable with a diameter of 10 mm, a typical breaking force is about 55-65 kN (it can be worse or better). Roughly, one kN corresponds to 100 kg of load mass. So consider that this is 5500-6500 kg and divide by the specific gravity.