Hint: Start by using this definition of force. Force is the time rate of change of momentum i.e.$F=dP/dt=d(mv)/dt=vdm/dt+mdv/dt$ the mass the force is lifting is changing. the mass at any given instant is $m=\frac{ M }{ L }x$ where x is the length of rope lifted. We also know $x=vt$ substitute and solve.