I Force exerted by a rope wound around a disk

The above picture shows the forces on a disk supported by a rope which is wound around it. The tension T is shown to be acting at the point where the rope loses contact with the disk. I think the reason for this is that the friction is assumed to be huge so that the tension in the rope also acts on the disk. But there is also the reaction from the rope and since the rope is wound around the entire circumference we may think that it cancels out but I think that the reaction from the rope at the bottom should be greater than at the top due to the weight of the disk. How to account for all these forces? And if it is true that the net force by the rope on the disk is just the tension T as shown then how can I prove it precisely?

 

Thank you very much. I completely missed that.