This is a question I found in a book:
A string is wrapped around a uniform cylinder as shown in diagram. When cylinder is released string unwraps without any slipping and the cylinder comes down.
I assumed that an equation $T - mg = ma$ could be formulated and the tension does negative work. However the answer is that the tension does zero work. This I understand is because the cylinder is in free fall, and the equation will be $T - mg = mg$ and therefore $T = 0$.
Is my assumption correct? If it is, why is this so? It doesn't make sense to me. Should the tension exert some upward force and the downward acceleration be at least a bit less than $g$?