Q. A partly hanging uniform chain of length 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
A) $\frac{l}{L - l}$
B) $\frac{L}{l}$
C) $\frac{l}{L}$
D) $\frac{lL}{L + l}$
Explanation
(a) 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, $\mu_{s}\mu(L - l)g = \mu lg$ or $\mu_{s} = \frac{l}{L - l}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.