A smooth cylinder is fixed with its axis horizontal. Radius of the cylinder is R. A uniform rope (ACB) of linear mass density `lambda` (kg/m) is exactly of length `pi`R and is held in semicircular shape in vertical plane around the cylinder as shown in figure. Two massless strings are connected at the two ends of the rope and are pulled up vertically with force `T_(0)` to keep the rope in contact with the cylinder.
(a) Find minimum value of `T_(0)` so that the rope does not lose contact with the cylinder at any point.
(b) If `T_(0)` is decreased slightly below the minimum value calculated in (a), where will the rope lose contact with the cylinder.

Answer

(a) `T_(0) = 2 lambda "Rg"`
(b) At the lower point