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
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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