A uniform metal chain of mass \(m\) and length ' \(L\) ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' \(l\) ' is hanging on one side and rest of its length ' \(L -l\) ' is hanging on the other side of the pulley. At a certain point of time, when \(l=\frac{L}{x}\), the acceleration of the chain is \(\frac{g}{2}\). The value of \(x\) is ........

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(D) \(4\)

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\(a =\frac{\left( m _{2}- m _{1}\right)}{\left( m _{2}+ m _{1}\right)} g\)

\(\frac{ g }{2}=\frac{(\lambda( L -\ell)-\lambda \ell) g }{\lambda L } \Rightarrow L =\frac{ L }{4}=\frac{ L }{ x }\)

\(x =4\)

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