Question

A uniform chain of length $\ell$ is placed on a rough table, with length $\ell /3$ hanging over the edge. If the chain just begins to slide off the table by itself from this portion, the coefficient of friction between the chain and the table is $1/K$. Then, find the value of $K$.

Answer 1

We know,

For this case to happen,

$F_g=f_{max}$

Let Linear mass density be $\lambda$

$\lambda \frac{l}{3}g=\mu \lambda \frac{2l}{3}g$

$\frac{1}{3}=\frac{1}{K}\frac{2}{3}$

$K=2$