A uniform chain of length L is lying partly on a table, the remaining part hanging down from the edge of the table. If the coefficient of friction between the chain and the table is 0.5 , what is the minimum length of the chain that should lie on the table, to prevent the chain from slipping down to the ground?

Step-by-step solution

Let length of chain lying the table be y . Mass per unit length of the chain = M L Mass of the chain lying on the table, M^ = M L y Mass of the length (L-y) of hanging chain = M L (L-y) At equilibrium, Friction force between table and chain = Weight of hanging part of the chain ( M L y ) g= M L (L-y) g y=L-y 0.5 y=L-y [ =0.5] y= 2 L 3