# Chain Please Don't Fall!

**Classical Mechanics**Level 5

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 :)