Problem 2.

1.      A smooth cylinder of radius a is fixed on a rough horizontal table with its axis parallel to the table. A uniform rod ACB of length 6a and mass M rests in limiting equilibrium with the end A on the table and the point C touching the cylinder. The vertical plane containing the rod is perpendicular to the axis of the cylinder and the rod makes an angle 2q with the table.

(a)  Show that the magnitude of the force exerted by the cylinder on the rod is

            3Mg cos 2q tan q

(b)  Show also that , the coefficient of friction between the rod and the table, is given by

                        (cot q - 3cos 2 q) = 3 sin 2 q cos 2 q


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