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Question

A uniform chain of length l is placed on the table in such a manner that length l of it is hanging over the edge of the table without the chain sliding. If the coefficient of friction between the chain and the table is μ then find the maximum length of chain l that can hang without the entire chain slipping.


A

0

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B

(μ+1)lμ

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C

lμ+1

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D

μl1+μ

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Solution

The correct option is D

μl1+μ




Assume the mass of the chain to be M kg.
The linear density of the chain is given by π=Ml
The mass of chain hanging is πl kg and the mass of chain on the table is π(ll) kg.
The only force pulling the chain on the table is the weight of the chain that is hanging.

For maximum hanging length without sliding,
fmax=πlg and
fmax=μN=μπ(ll)g
πlg=μπ(ll)g
l=μl1+μ


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