question_answer

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:

                Let y be the maximum length of the chain, which can be held outside the table without sliding. Length of the chain oh the table = (L - y)               Weight of this part of chain = \[W=\frac{M}{L}yg\]                           Weight of hanging part-pf chain = \[W'=\frac{M}{L}\left( L-y \right)g\] For equilibrium, Fig. 3(HT).7    force of fraction (j) = wt. of hanging part of chain \[\mu R=W\] \[\mu W'=W\] \[\mu .\frac{M}{L}\left( L-y \right)g=\frac{M}{L}yg\] \[\mu Mg-\mu \frac{Myg}{L}=\frac{M}{L}yg\] \[\mu Mg=\frac{M}{L}yg\left( 1+\mu  \right)\] \[y=\frac{\mu L}{\left( 1+\mu  \right)}\]