Question 155 of 210

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 _____ $m$.

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Answer: 2

Let, $\lambda =$mass per unit length of the chain and length of mass hanging through the table is $x$.

Normal force applied by the table on the chain will be, $N=\left(l-x\right)\lambda g$.
Tension developed in the chain will balance the gravitational force acting in the downward direction, $T=\lambda xg$.
Maximum limiting force possible for the part of the table, ${f}_{max}=\mu N=\mu \left(l-x\right)\lambda g$
For equilibrium,
${f}_{max}=T$,
$\Rightarrow \mu \left(l-x\right)\lambda g=\lambda xg \Rightarrow \dfrac{1}{2}\times \left(6-x\right)=x\Rightarrow x=2m$