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. l′πg=fmax =μN =μ(l−l′)πg(asN=(l−l′)πg) ⇒l′πg=μπg(l−l′) ⇒l′=μ(l−l′) ⇒l′+μl′=μl ⇒l′=μl1+μ

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