A classical mechanics problem by Md Zuhair

A plank of mass M M is placed over a smooth triangular wedge with an angle of inclination 3 0 30^\circ . A block of mass m m is connected to the plank by a massless string . a cylinder of mass M M and radius R 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 = 4 m M=4m , find the angular acceleration α \alpha of the cylinder .

7g/6R 6g/7R 3g/2R 4g/3R 2g/13R 2g/9R

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