Q. 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%
Explanation

(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
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$\therefore$ 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
$\frac{mx}{l}.g = \mu\frac{m}{l}(l - x)g = 0.25\frac{m}{l}(l - x)g$
$\Rightarrow \ x = \frac{l}{5}$ or $\frac{x}{l} = \frac{1}{5} = 20\%$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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