# What a chain! 4

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 $$(t)$$

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

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!

×