Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $\left(l_2-l_1\right)$ is maintained same at all temperatures, which one of the following relations holds good?

  • [NEET 2016]
  • [AIPMT 1999]
  • A

    ${ \alpha _1}{l_2}^2 = \;{ \alpha _2}{l_1}^2$

  • B

    ${ \alpha_1}^2{l_2} =\;\;{ \alpha_2}^2 {l_1}$

  • C

    ${ \alpha _1} {l_1} ={ \alpha _2} {l_2}$

  • D

    ${ \alpha_1} {l_2}={ \alpha _2} {l_1}$

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