A chain of length L has some of its portion hanging vertically over the edge of the rough horizontal table of coefficient of friction μ. Find the greatest length of the chain that can hang without slipping.

Solution

Let x be the maximum length of the chain that can hang without slipping.

Therefore weight of hanging part of the chain is,

straight W subscript 1 space equals space λxg

where,
A, is the linear mass density of the chain.

Weight of the chain on the table is,

straight W subscript 2 space equals space straight lambda left parenthesis straight L space minus space straight x right parenthesis space straight g

The chain is just at the point of slipping when,

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