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Question

A uniform chain of length l is placed on the table in such a manner that its l' part is hanging over the edge of 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

lμ+1

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C

lμ+1

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D

μlμ+1

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Solution

The correct option is D

μlμ+1


The only force pulling the chain on the table is the weight of the chain that is hanging.

For maximum hanging length without sliding.

lπg=fmax

=μN

=μ(ll)πg(asN=(ll)πg)

lπg=μπg(ll)

l=μ(ll)

l+μl=μl

l=μl1+μ


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