At what temperature (in $ ^{\circ} C$) a gold ring of diameter $6.230$ $cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 \,cm$ ? Both the diameters have been measured at room temperature $\left(27^{\circ} C \right)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}$ )

  • [JEE MAIN 2022]
  • A

    $125.7$

  • B

    $91.7$

  • C

    $425.7$

  • D

    $152.7$

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