The correct answer is: D. Half the weight of the cable.
A suspended cable with supports at two ends is in equilibrium under the action of its own weight and the two support reactions. The support reactions are equal in magnitude and opposite in direction, and they act at the points of support. The weight of the cable acts vertically downwards through its center of mass.
The minimum pull in the cable is the resultant of the two support reactions and the weight of the cable. The resultant is a vertical force that acts through the center of mass of the cable. The magnitude of the resultant is equal to half the weight of the cable.
Option A: Horizontal thrust is not a force that acts on a suspended cable.
Option B: Support reactions are the forces that the supports exert on the cable. They are equal in magnitude and opposite in direction.
Option C: The resultant of the horizontal thrust and the support reaction is a vertical force that acts through the center of mass of the cable. The magnitude of the resultant is equal to half the weight of the cable.
Option D: Half the weight of the cable is the magnitude of the resultant of the two support reactions and the weight of the cable.