Final answer:
The statement that the horizontal thrust at the ends of a cable is inversely proportional to the sag of the cable is true. As the sag increases, the tension decreases, leading to a smaller horizontal thrust.
Step-by-step explanation:
The horizontal thrust at the ends of a cable is inversely proportional to the sag of the cable. Hence, the statement 'the greater the sag, the smaller the thrust' is true. Tension is the pulling force that acts along a stretched flexible connector, such as a rope or cable. When the cable is more horizontal, there is less sag, and the tension (and therefore the horizontal thrust) will be larger. However, a perfectly flexible connector experiencing no sag would require an infinite tension to remain perfectly horizontal, which is practically impossible. Therefore, with an increase in sag, the angle increases and since tension is proportional to the sine of the angle, tension decreases with an increase in sag, resulting in a smaller horizontal thrust.