Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the mid point of $PQ.$ Distance $OR$ remains same for small change in temperature. Coefficient of linear expansion for $PR$ and $RQ$ is same i.e. ${\alpha _2}$ but that for $PQ$ is ${\alpha _1}$. Then relation between ${\alpha _1}$ and ${\alpha _2}$ is

65-23

  • A

    ${\alpha _2} = 3{\alpha _1}$

  • B

    ${\alpha _2} = 4{\alpha _1}$

  • C

    ${\alpha _1} = 3{\alpha _2}$

  • D

    ${\alpha _1} = 4{\alpha _2}$

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