What a chain! 4

A chain of uniform mass density λ\lambda and mass MM and length LL is hanging from ceiling through a string. The other end of the chain is held at rest at the position shown in the figure. At time t=0t=0 the held part of chain is left to fall under gravity. Find the tension in the string as a function of time (t)(t) (neglecting friction). Your answer can be represented as

T(t)=Mga+bMg2t2cLT(t) = \frac{Mg}{a} + \frac{b Mg^2t^2}{c L}

where aa, bb, and cc are positive coprime integers. Enter your answer as a+b+ca + b + c.

Note: Figures are not to scale.

This is inspired by Depanshu's Chain please don't fall! and is a part of my set Aniket's Mechanics Challenges.


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