Two identical rough boards are attached to a horizontal fixed axle. Friction between the boards and the axle is negligible. Both boards have a mass $m$ and a length $l$. A cylinder of mass $M=m/2$ and radius $R=l/5$ is placed between the boards.
1
What must the least value of the coefficient of static friction between the planks and the cylinder be so that the cylinder can remain in equilibrium somewhere (at a suitably chosen point)?
2
What can the angle subtended by the boards be when the cylinder is in equilibrium?
