Assuming the length of a chain to be L and coefficient of static friction `mu`. Compute the maximum length of the chain which can be held outside a table without sliding.

Explanation

Let y be the maximum length of the chain can be hold out side the table without sliding.
Length of chain on the table `=(L-y)`
Weight of part of the chain on table `W'=(M)/(L)(L-y)g`
Weight of hanging part of the chain `W=(M)/(L)yg`
For equilibrium: limiting force of friction=weight of hanging part of the chain
`muR=W rArrmuW=WrArrmu(M)/(L)(L-y)g=(M)/(L)ygrArrmuL-muy=yrArry=(muL)/(1+mu)`