Assuming the length of a chain to be L and coefficient of static friction mu calculate the maximum length of the chain which can be held outside a table without sliding ?

Assuming the length of a chain to be L and coefficient of static frict

1.	Assuming the length of a chain to be L and coefficient of static friction mu calculate the maximum length of the chain which can be held outside a table without sliding ?
Answer» Solution :Let y be the MAXIMUM length of the chain, which can be HELD outside the table WITHOUT SLIDING Length of the chain on the table `= (L-y)` Weight of this part of chain `W = (M)/(L) (L-y) g` Weight of hanging part of chain `= W= (M)/(L) yg` For equilibrium force of FRICTION `(f) = wt` of hanging part of chain `mu R = W` `mu W =W ` `mu (M)/(L) (L-y) g = (M)/(L) yg` `mu Mg - mu (M yg)/(L) = (M)/(L) gy, mu Mg = (M)/(L) yg (1 + mu)` `y = (mu L)/((1 + mu ))` .