Question

A chain of length $L$ starts sliding down from the horizontal surface of a table. If the hanging length is $l$, the coefficient of friction between the table and chain is:

• A. $\frac{l}{L}$
• B. $\frac{L}{l}$
• C. $\frac{l}{L-l}$
• D. $\frac{L-l}{l}$

Answer 1

Answer: (C)

$\frac{l}{L-l}$

Mass per unit length is $\frac{m}{L}$

Mass of the part on the table$=\frac{m}{L}(L-l)$

Mass of the hanging part$=\frac{m}{L}\left(l\right)$

Friction balances the weight of the part that is hanging:
$\mu \frac{m}{L}(L-l)g=\frac{m}{L}\left(l\right)g$

$\mu =\frac{l}{L-l}$