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 µ,
the coefficient of friction between the rod and the table, is
given by

µ(cot q - 3cos² 2 q) = 3 sin 2 q cos 2 q