A metallic rod $1\,cm$ long with a square cross-section is heated through $1^o C$. If Young’s modulus of elasticity of the metal is $E$ and the mean coefficient of linear expansion is $\alpha$ per degree Celsius, then the compressional force required to prevent the rod from expanding along its length is :(Neglect the change of cross-sectional area)

  • A

    $EA\alpha t$

  • B

    $EA\alpha t/(1 + \alpha t)$

  • C

    $EA\alpha t/(1\alpha t)$

  • D

    $E/\alpha t$

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