A cylindrical container, $0\mathrm{.}3$ m diameter, $0\mathrm{.}6$ m high, has two third of its height filled with oil of relative density $0\mathrm{.}8.$ The container is rotated about its vertical axis. Determine the speed of rotation when $($a$)$ the oil just starts spilling over, and $($b$)$ the centre of the base is just exposed. In $($b$),$ find the percentage of oil still left in the container.