We're told that the cylinder is in midair.
This implies that the center of mass of the cylinder is at rest.
Let's consider Newton's second law of motion.
A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval delta-t and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is 1/2MR^2
The net force on the cylinder during the time interval delta-t is?
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