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 co-efficient 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.......\(m.\)

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(D) \(2\)

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Mass per unit length \(=\lambda\)

\(N = mg =\lambda( L - x ) g\)

\(fs _{\max }=\mu_{ s } N\)

\(fs _{\max }=(0.5)(\lambda)( L - x ) g\)

And also \(fs _{\max }= m _{ x } g\)

\(0.5 \lambda( L - x ) g =\lambda xg\)

\(\frac{ L - x }{2}= x\)

\(\frac{ L }{2}=\frac{3 x }{2} \Rightarrow x =\frac{ L }{3}=\frac{6}{3}=2 \,m\)

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