A uniform chain of 6m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is ______

Let the length of the chain hanging be 'l', and the linear mass density be $\lambda$

So the tension in the chain at the end of the table will be the weight of the chain that is hanging.

This weight is balanced by the friction force acting on the chain that is present on the table.

The frictional force is given by $\mu (6-l)\lambda g$.

$\Rightarrow \mu (6-l)\lambda g=\lambda lg\Rightarrow 0.5(6-l)=l$

$\Rightarrow l=2m$