Question

There is uniform chain of mass $m$ and length $\ell$ on the rough table having coefficient of friction $\mu$ . Find out the maximum length which can be suspended such that chain does not slide down.

Answer 1

The hanging chains weight gets balanced by the friction by the chain lying on the surface.

Mass per unit length will be $\frac{m}{l}$

So the weight of hanging part will be $\frac{m}{l}gx$

And the friction provided by the chain lying on the surface will be $\mu \frac{m}{l}g\left(l-x\right)$

Both the forces will be equal,

So,

$\mu \frac{m}{l}g\left(l-x\right)=\frac{m}{l}g\left(x\right)$

$x=\frac{\mu }{\mu +1}lunits$