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When the hanging weight in a pulley system is halved, the tension in the system decreases. This is due to the relationship between the weight applied and the force exerted on the rope.

In a typical pulley system, the tension in the rope is directly related to the weight that it is supporting. When the weight is reduced, there is less gravitational force acting on the system. Specifically, tension is calculated as the force needed to balance the weight being supported. With a smaller weight, the required force (or tension) to keep the system balanced also reduces.

Therefore, when the hanging weight is halved, the downward force decreases, leading to a corresponding decrease in tension within the rope. This fundamental concept of mechanics illustrates how weights and forces interact within a pulley system, reinforcing the understanding of principles like equilibrium and force balance.