Why is work done by tension in pulley system zero ?

Net work done by tension of an ideal thread on its adjoining bodies is always zero. Ideal thread means it is massless and inextensible. So for such a thread, tension at each and every point of the thread would be same. Also since the thread is inextensible, so for it to remain always taut, the displacements of both the ends of the thread (along the thread) in any time interval should be equal. Further the tension force applied by the thread on its adjoining bodies are equal in magnitude but are relatively opposite in direction (tension is a force of pulling nature, so it always pulls the objects attached to it).

The above discussion concludes following two things:

• Tension at both the ends of the thread are equal but they act relatively opposite to each other.
• Displacements of both the ends of the thread along the thread are equal.

Therefore work done ( F. ds ) at one end is negative of the work done at the other end. In other words work done (by the tension) at one end is positive and the same at the other end is negative but magnitude-wise both are same. Hence total work done by tension of an ideal thread/ rope is always zero. The statement applies to all the physical systems involving ideal string(s).