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  4. A partly hanging uniform chain of length L is resting on a rough horizontal table. l is the maximum possible length that can hang in equilibrium. The coefficient of friction between the chain and table is

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Q. A partly hanging uniform chain of length $L$ is resting on a rough horizontal table. $l$ is the maximum possible length that can hang in equilibrium. The coefficient of friction between the chain and table is

Laws of Motion

Solution:

If $\mu$ is the mass/length, then
Weight of hanging length $=\mu\, lg $
Weight of chain on table $=\mu(L-l) g$
$R=\mu(L-l) g$
$f=\mu_{s} R=\mu_{s} \mu(L-l) g$
Equating, $\mu_{s} \mu(L-l) g=\mu l g$
or $\mu_{s}=\frac{l}{L-l}$