If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected so that total length becomes $3L$, the average coefficient of linear expansion of the composition rod equals:

  • A

    $\frac{3}{2}\alpha $

  • B

    $\frac{5}{2}\alpha $

  • C

    $\frac{5}{3}\alpha $

  • D

    none of these 

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