Question

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

• A. $20 \%$
• B. $25 \%$
• C. $35 \%$
• D. $15 \%$

Answer 1

Answer: (A)

Let length of chain be $l$ and mass $m$. Let a part $x$ of chain can hang over one edge of table having coefficient of friction.

$\therefore $ Pulling force, $F=\frac{m x}{l} g$
and friction force, $f=\mu N=\mu \frac{m}{l}(l-x) g$
For equilibrium, $F=f$, hence
$ \frac{m x}{l} \cdot g=\mu \frac{m}{l}(l-x) g=0.25 \frac{m}{l}(l-x) g $
$\Rightarrow x =\frac{1}{5} $
or $\frac{x}{l}=\frac{1}{5}=20 \%$