A uniform chain of length L is kept on a table of coefficient of stati

1.	A uniform chain of length L is kept on a table of coefficient of static friction μ(limiting value). Find the maximum length of chain that can be outside the table, without it sliding away.
Answer» Let x be the length of the chain that can be outside the table. Let ‘M’ be the total mass of the chain. Mass on the table is \(\frac {M}{L}\) (L – x) Mass of the chain outside = \(\frac {M}{L}\) x For, equilibrium, Force of friction = weight of the hanging part. .e., μN = \((\frac {M}{L}x)\) g × α i.e., μ \((\frac {M}{L}(L-x)g) = (\frac {M}{L}x)\)g μ(L – x) = x or x = \(\frac {μL}{1+μ}\).

A uniform chain of length L is kept on a table of coefficient of static friction μ(limiting value). Find the maximum length of chain that can be outside the table, without it sliding away.

Answer»

Let x be the length of the chain that can be outside the table. Let ‘M’ be the total mass of the chain.

Mass on the table is \(\frac {M}{L}\) (L – x)

Mass of the chain outside = \(\frac {M}{L}\) x

For, equilibrium,

Force of friction = weight of the hanging part.

.e., μN = \((\frac {M}{L}x)\) g × α

i.e., μ \((\frac {M}{L}(L-x)g) = (\frac {M}{L}x)\)g

μ(L – x) = x or x = \(\frac {μL}{1+μ}\).