Lifting Rope.

A rope of length ll and mass density λ\lambda lies in a heap on a floor. You grab one end of the rope and pull upward with a non-impulsive constant force Fo{ F }_{ o }. Find the time period require to completely lift off the rope.

Assume that the rope is greased.

The answer is in the form T=ag(FoλFoλbglc)\displaystyle{{ T=\cfrac { a }{ g } (\sqrt { \cfrac { { F }_{ o } }{ \lambda } } -\sqrt { \cfrac { { F }_{ o } }{ \lambda } -\cfrac { bgl }{ c } } })}

Find a+b+ca+b+c

I got this question from Deepanshu.

:D

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