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 μ then find the maximum length of chain l' that can hang without the entire chain slipping.
μlμ+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′πg=fmax
=μN
=μ(l−l′)πg(asN=(l−l′)πg)
⇒l′πg=μπg(l−l′)
⇒l′=μ(l−l′)
⇒l′+μl′=μl
⇒l′=μl1+μ