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A heavy uniform chain lies on horizontal table top. If the co-efficient of friction between the chain and the table surface is $0.25$ , the maximum percentage of the length of the chain that can hang over one edge of the table is

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$25 %$

$20 %$

$35 %$

$15 %$

answer is A.

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Detailed Solution

Let $l$ be the length hanging freely

For equilibrium :

$μ M (\frac{L - l}{L}) g = M (\frac{l}{L}) g$

$\Rightarrow μ (L - l) = L \Rightarrow \frac{L - l}{l} = \frac{1}{μ}$

$\frac{L}{l} = \frac{1 + μ}{μ} \Rightarrow \frac{l}{L} = \frac{μ}{1 + μ} = \frac{1}{5}$

Percentage hanging = 20%

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