Final answer:
The height of a cable in a cable bridge is not independent of the length along the cable. This means that changing the length of the cable will have an impact on its height. Similarly, the height of a cable is not determined solely by its length, as there are other factors that influence it. These factors include the cable's tension and the weight it is supporting, thus the correct option is D.
Step-by-step explanation:
The height of a cable in a cable bridge is not independent of the length along the cable. This means that changing the length of the cable will have an impact on its height. Similarly, the height of a cable is not determined solely by its length, as there are other factors that influence it. These factors include the cable's tension and the weight it is supporting. Therefore, the correct answer is option D) The cable's height is inversely proportional to its length.
To understand this concept better, let us take a closer look at the relationship between the height and length of a cable in a cable bridge. According to the inverse proportionality rule, as one quantity increases, the other quantity decreases in proportion. In this case, as the length of the cable increases, the height of the cable decreases, and vice versa. This is because as the cable becomes longer, it needs to be supported by more tension, which causes it to sag and decrease in height.
To illustrate this, let us consider a simple hypothetical scenario. Imagine a cable bridge with a length of 100 meters and a height of 10 meters. Now, if we increase the length of the cable to 200 meters while keeping the tension and weight constant, the height of the cable will decrease to 5 meters. This is because the longer cable needs more tension to support its weight, resulting in a decrease in its height. Similarly, if we decrease the length of the cable to 50 meters, its height will increase to 20 meters.
This relationship between the height and length of a cable is crucial during the construction and maintenance of cable bridges. Engineers need to carefully consider the length of the cable and the tension required to support it to ensure the safety and stability of the bridge. Any miscalculations in these factors can result in a cable bridge collapsing, posing a threat to public safety.
In conclusion, the correct answer to the given question is option D) The cable's height is inversely proportional to its length. The height of a cable in a cable bridge is not independent of its length and is determined by factors such as tension and weight. This inverse proportionality relationship between the height and length of a cable is crucial in the construction and maintenance of cable bridges, ensuring their safety and stability.