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Question

# A uniform chain of length â€²lâ€² is placed on a rough table, with its length ln(n>1) hanging over the edge of the table. If the chain just begins to slide off the table by itself, the coefficient of friction between the chain and the table is:

A
1n+1
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B
1n1
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C
n1n+1
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D
1n
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Solution

## The correct option is B 1n−1In this case, the weight of the hanging part must be just equal to the frictional force acting on the part on the table.We know that, F=μNLet linear mass density be γ.Mass of the chain on the table is m′=l(1−1n)γFrictional force, μN=μγ(l−ln)g, where, γ is the linear mass density of the chain.Weight of the hanging part, W=γlngEquating the above two equations yield,μ=1n−1

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