A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The coefficient of static friction between the chain and

Question

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The coefficient of static friction between the chain and the surface of the table is 0.5 , the maximum length of the chain hanging from the table is ____ m.

TestHub · Accepted Answer

Let y be the suspended length Mass per unit length of chain $= \frac{M}{6}$ Mass of the suspended part $= \frac{M}{6} y$ For equilibrium of chain, the weight of suspended part must be balanced by force of friction on the portion on the table.

$μ N = \frac{M}{6} y g$

$μ \frac{M ( 6 - y ) g}{6} = \frac{M}{6} y g$

$\frac{1}{2} (6 - y) = y \Rightarrow (6 - y) = 2 y$

$3 y = 6 \Rightarrow y = 2 m$

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