A chain of length L rests on a rough table. If μ be coefficient of friction, maximum friction

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4-2.Friction

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A chain of length $L$ rests on a rough table. If $\mu $ be the coefficient of friction, the maximum friction of the chain that can hang over the table will be

A

$\frac {\mu -1}{\mu }$

B

$\frac {\mu }{\mu +1}$

C

$(\mu -1)$

D

$\frac {1}{\mu +1}$

Solution

Let $m$ be the mass per unit length of the chain.

Suppose the length of the hanging chain is $l.$ Then,

$\mu(\mathrm{L}-\ell) \mathrm{mg}=\ell \mathrm{mg}, \mu \mathrm{L}=(\mu+1) \ell$

$\therefore \frac{\ell}{L}=\frac{\mu}{\mu+1}$

Standard 11

Physics

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