A classical mechanics problem by Md Zuhair

A plank of mass $$M$$ is placed over a smooth triangular wedge with an angle of inclination $$30^\circ$$. A block of mass $$m$$ is connected to the plank by a massless string . a cylinder of mass $$M$$ and radius $$R$$ is now placed over the plank, such that one end of the string , wrapped over cylinder is fixed and parallel to incline . friction is sufficient enough for pure rolling of cylinder. If the system is released from rest with condition that $$M=4m$$ , find the angular acceleration $$\alpha$$ of the cylinder .

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