A heavy uniform metal chain is kept on the surface of a horizontal table. The coefficient of friction between the chain and the table surface is 0.22. Find the maximum fraction of length of the chain that could hung over on one edge of the table ?

A heavy uniform metal chain is kept on the surface of a horizontal tab

1.	A heavy uniform metal chain is kept on the surface of a horizontal table. The coefficient of friction between the chain and the table surface is 0.22. Find the maximum fraction of length of the chain that could hung over on one edge of the table ?
Answer» Solution :Let L be the total length of the chain, l that of the hanging PART of the chain and m the massper UNIT length of the chain. When the chain is in equilibrium, Weight of the hanging part `=` Frictional FORCE between chain and the table `mlg=mu m(L-l)g` `l=muL-mul` `l(1+mu)=muL` Fraction of length of chain `=(l)/(L)=(mu)/(1+mu)=(0.22)/(1+0.22)=0.18=18%`