Chain Please Don't Fall!

A uniform chain of length "L" and mass per unit length is "\(\lambda \)" is suspended at one end A by inextensible light string and the other end of the chain B is held at rest at the level of end A of the chain (As Shown ). Now The end B of the chain is released under gravity then find the tension in the string at the moment when end B as fallen by distance "y" .

If Tension is expressed as :

\[T(y)\quad =\quad \cfrac { \lambda g }{ a } (L\quad +\quad by)\].

Then Evaluate the value of "a + b" ?

\(\bullet \) Where "a" and "b" are positive co-prime integers .

\(\bullet \) Figure is not drawn to scale .

\(\bullet \) Variable mass concept Might Be helpful here :)

This is part of my set Deepanshu's Mechanics Blasts

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