# What a chain! 4

**Classical Mechanics**Level 5

A chain of uniform mass density \(\lambda\) and Mass \(M\) and length \(L\) is hanging from ceiling through a string. The other end of the chain is held at rest at the position shown in the figure.

Now the held part of chain is left to fall under gravity .

Find the tension in the string as a function of time \((t)\)

Your answer can be represented as

\( T(t) = \) \(\frac{Mg}{a}\) \(+\) \(\frac{b Mg^2t^2}{c L}\)

where \(a\) , \(b\) , \(c\) are positive integers.

Enter your answer as \(a + b + c\).

**Details and Assumptions**:

At \(t = 0\) the chain is just left to fall under gravity.

Neglect friction.

Figure is not to scale.

\(c\) and \(b\) are positive coprime integers.

Inspired by Depanshu's Chain please don't fall!

#### This is a part of my set Aniket's Mechanics Challenges

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