tension on the rope

A uniform solid cylinder of mass m rests on two horizontal planks . A thread is wound on the cylinder . The hanging end of the thread is pulled vertically down with a constant force 'F' find the maximum magnitude of the force 'F' there is no sliding and coefficient of friction is'k'

3mgk/(2-3k) 2mg/(3-2k) mg/k 9mg/2k

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