Final answer:
Tension in the string during horizontal circular motion is equivalent to the centripetal force because it counters the object's inertia, which would otherwise cause it to move in a straight line. The tension, acting toward the center of the circle, keeps the object in its circular path, consistent with Newton's third law of motion.
Step-by-step explanation:
The tension in the string during the horizontal circular motion of a mass is equivalent to centripetal force because it is this force that keeps the object moving in a circular path. According to Newton's third law of motion, every action has an equal and opposite reaction. When an object moves in a circular motion, it tends to move outward due to inertia; however, the string provides the necessary inward force (tension) which acts as the centripetal force. The physical origin of the force stretching the string is the inertia of the mass, which would move in a straight line if not for the tension in the string redirecting it toward the center of rotation.
For example, when a ball tied to a string is swung in a circle, the ball exerts an outward force due to its inertia, which is matched by the tension in the string pulling in the opposite direction. This tension is what keeps the ball moving in a circle and not flying off in a tangent to the circular path. The tension must be equal to the required centripetal force to maintain this circular motion without the string breaking or the object escaping the circular path.