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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