A block of mass $11{\text{ }}kg$ is at rest on a rough plane inclined at ${30^ \circ }$ to the horizontal. A force acts on the block in a direction up the plane parallel to a line of greatest slope. When the magnitude of the force is $2X{\text{ }}N$ the block is on the point of sliding down the plane, and when the magnitude of the force is $9X{\text{ }}N$ the block is on the point of sliding up the plane. Find
a) the value of $X$,
b) the coefficient of friction between the block and the plane.
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