A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of Elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to

  • [JEE MAIN 2019]
  • A

    $9F/\left( {\pi {r^2}YT} \right)$

  • B

    $F/\left( {3\pi {r^2}YT} \right)$

  • C

    $3F/\left( {\pi {r^2}YT} \right)$

  • D

    $6F/\left( {\pi {r^2}YT} \right)$

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