A uniform rope of length has been placed on fixed cylinder of radius R as shown in the fig. One end of the rope is at the top of the cylinder. The coefficient of friction between the rope and the cylinder is just enough to prevent the rope from sliding. Mass of the rope is M.
(a) At what position, the tension in the rope is maximum?
(b) Calculate the value of maximum tension in the rope.
In the last problem, the rope is placed on the cylinder as shown. Find maximum tension in the горе.

A tube of mass M hangs from a thread and two balls of mass m slide inside it without friction (see figure). The balls are released simultaneously from the top of the ring and slide down on opposite sides. O defines the positions of balls at any time as shown in figure.

(a) Show that ring will start to rise if m≥ 3M/2(b) If M = 0, find the angle at which the tube begins to rise.










































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