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A plank of mass $$M$$ and length $$L$$ is at rest on a frictionless floor. The top surface of the plank has friction. At one end of it a man of mass $$m$$ is standing as shown in Fig. If the man walks towards the order end, find the distance, which the plank moves(a) till the man reaches the centre of the plank, (b) till the man reaches the other end of the plank.

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