A one-piece cylinder has a core section protruding from the larger drum and is free to rotate around its central axis. A rope wrapped around the drum of radius 1.05 m exerts a force of 3.33 N to the right on the cylinder. A rope wrapped around the core of radius 0.45 m exerts a force of 6.77 N downward on the cylinder.

Explanation:

First, we will calculate the torque because of the rope wrapped around the drum as follows.

    torque1, =

                        = 3.496 N m

Now, we will calculate the torque because of the rope around the core as follows.

    torque2, =

                       = 3.046 N m

(Since, we are provided with any figure which means that the torque can act either in the same direction or in the opposite direction.)

So, if the torque is acting in the same direction then,

       torque = torque1 + torque2

                  = (3.496 + 3.046) N m

                  = 6.542 Nm

And, if the torque is acting in the opposite direction then,

      torque = torque1 - torque2

                  = (3.496 - 3.046) Nm

                  = 0.45 Nm

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