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