Question

A uniform chain is just at rest over a rough horizontal table with its $\frac{I}{\eta }th$ part of length hanging vertically. Find the of co-efficient of static friction between the chain and the table.

Answer 1

R.E.F image

Total Length L

Linear mass density $\lambda =\frac{M}{L}$

mass of hanging portion $=\lambda \frac{L}{n}$

$=\frac{M}{n}$

Mass of charh on table $=\lambda (L-\frac{L}{n})$

$=m\frac{(n-1)}{n}$

As it just rest over table $f=$ weight of hanging portion

$\mu \left(N\right)=\frac{M}{n}g$

$\mu M\frac{(n-1)}{n}g=\frac{M}{n}g$

$\mu =\frac{1}{n-1}$ Ans