Question

A uniform rope of length $l$ lies on a table. If the coefficient of friction is $\mu $ , then the maximum length $l_{1}$ of the part of this rope which can overhang from the edge of the table without sliding down is

• A. $\frac{1}{\mu }$
• B. $\frac{l}{\mu + 1}$
• C. $\frac{\mu l}{1 + \mu }$
• D. $\frac{\mu l}{1 - \mu }$

Answer 1

Answer: (C)

Weight of hanging part is balanced by friction
$\left(m \frac{l_{1}}{l}\right)g=\mu N$
$\left(m \frac{l_{1}}{l}\right)g=\mu \left(m \frac{l - l_{1}}{l}\right)g$
$l_{1}=\mu \left(l - l_{1}\right)$
$l_{1}=\frac{\mu l}{\mu + 1}$