What is the free-body diagram for a massless pulley in free fall?

[Lnewqban]

I agree which makes it confusing that mass-less pulleys and strings are used to teach Newtonian mechanics !

Hope we are not confusing you even more going deeper into the subject.

Also, levers, gears, wedges, belts and slopes, and any part of simple machines, are frequently assumed to have negligible mass, for the very same reasons of simplifying calculations and eliminating the effect of their individual accelerations. By doing so, we devote our neurones solely to the effect of the mechanical energy input into the system on the relatively big and important masses.

Please, see:
https://en.m.wikipedia.org/wiki/Simple_machine

Same concept applies to deflection, stretching, friction and wear of those parts.
In order to make the learning process less confusing, we want to imaging that exactly the same amount of energy or work put into the simple machine goes out at the opposite end of it.

In the case of ideal problems involving mechanical advantage (MA), we assume a theoretical efficiency of 100%.
In practical or experimental problems, where the above assumptions can’t be made, there is a practical MA which magnitude is always less than the ideal MA.

 

[Nugatory]

I agree which makes it confusing that massless pulleys and strings are used to teach Newtonian mechanics !

Yes, and the only reason we can get away with it is that they’re always attached to something with non-zero mass and we’re applying a force to the whole thing.