Question

A uniform chain of length l is placed on the table in such a manner that its l' part is hanging over the edge of table without the chain sliding. If the coefficient of friction between the chain and the table is $\mu$ then find the maximum length of chain l' that can hang without the entire chain slipping.

• A. 0
• B. $\frac{l}{\mu +1}$
• C. $\frac{l}{\mu +1}$
• D. $\frac{\mu l}{\mu +1}$

Answer 1

The correct option is D

$\frac{\mu l}{\mu +1}$

The only force pulling the chain on the table is the weight of the chain that is hanging.

For maximum hanging length without sliding.

$l^{\prime }\pi g=f_{max}$

=$\mu$N

=$\mu (l-l^{\prime })\pi g(asN=(l-l^{\prime }\left)\pi g\right)$

$\Rightarrow l^{\prime }\pi g=\mu \pi g(l-l^{\prime })$

$\Rightarrow l^{\prime }=\mu (l-l^{\prime })$

$\Rightarrow l^{\prime }+\mu l^{\prime }=\mu l$

$\Rightarrow l^{\prime }=\frac{\mu l}{1+\mu }$