Final answer:
A cable or chain hung freely under gravity assumes a shape called a catenary, with the tension in the cable being directly related to its weight when supporting a load.
Step-by-step explanation:
The shape which a cable assumes when the only load acting on it is its own weight is called a catenary. In the context of physics, this shape is significant because it is the equilibrium shape for a flexible chain or cable that is suspended by its ends and subjected to a uniform gravitational force. The tension in a cable, T, is the pulling force that acts along a stretched flexible connector and is equal to the weight of the object it supports (T = mg) when the object is at rest. When considering only the weight of the chain or cable, which is distributed along its length, the curve formed is described mathematically by a hyperbolic cosine function, demonstrating the relationship between tension and weight distribution.