# Why work done by tension (like string force) is always zero?

A fixed disc free to rotate about its center (a flywheel) has a string wrapped around it, with a block attached to it. As the block falls, The tension in the string makes the disc rotate. Now, when the disc rotates by an angle $$\theta$$ (assuming the string doesn't slip), a length $$r\theta$$ of string unwraps. The length of the piece of string which is attached to the block is changing. Why is work done by tension (on block + disc system) zero?

I don't get it.

So if I'm using the energy theorem in this system that states:

Variation of energy = Work done by string tension (considering that the tension here is the only non conservative force) = 0?! Because work done by tension is zero?

[Here is the system]