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 ........

209767-q

  • [JEE MAIN 2022]
  • A

    $6$

  • B

    $2$

  • C

    $1.5$

  • D

    $4$

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