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Question

A uniform chain of length l 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 1n1
In 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=μN
Let linear mass density be γ.
Mass of the chain on the table is m=l(11n)γ

Frictional force, μN=μγ(lln)g, where, γ is the linear mass density of the chain.

Weight of the hanging part, W=γlng

Equating the above two equations yield,

μ=1n1



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