A force is applied to a steel wire ' $A$ ', rigidly clamped at one end. As a result elongation in the wire is $0.2\,mm$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be $............\times 10^{-2}\,mm$ (wires having uniform circular cross sections)

  • [JEE MAIN 2023]
  • A

    $6.06$

  • B

    $2.77$

  • C

    $3.0$

  • D

    $6.9$

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  • [AIEEE 2012]