Final answer:
The situation where the net external force on a system is not zero while maintaining a constant speed is known as uniform circular motion. Here, the centripetal force causes centripetal acceleration towards the center, which changes the direction but not the speed of the object.
Step-by-step explanation:
One situation where the net external force on a system is not zero, yet its speed remains constant, is uniform circular motion. An object moving in a circular path at a constant speed experiences a continuous change in direction, which means there is an acceleration. This acceleration, called centripetal acceleration, is directed towards the center of the circular path and is caused by a centripetal force, which is the net force. According to Newton's second law of motion, net force is mass times acceleration (net F = ma), and for uniform circular motion, this force is always directed towards the center, keeping the speed constant while changing the direction of the velocity.
The best answer to the question describing a situation where the net external force is nonzero but the object's speed remains constant is (a) Uniform circular motion.