In a typical combustion engine the work done by a gas molecule is given $W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be

  • [JEE MAIN 2021]
  • A

    $\left[ MLT ^{-2}\right]$

  • B

    $\left[ M ^{0} LT ^{0}\right]$

  • C

    $\left[ M ^{2} LT ^{-2}\right]$

  • D

    $\left[ MLT ^{-1}\right]$

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Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :

List $I$ List $II$
$P.$ Boltzmann constant $1.$ $\left[ ML ^2 T ^{-1}\right]$
$Q.$ Coefficient of viscosity $2.$ $\left[ ML ^{-1} T ^{-1}\right]$
$R.$ Planck constant $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$
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Codes: $ \quad \quad P \quad Q \quad R \quad S $ 

  • [IIT 2013]