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An expression for a dimensionless quantity P, given by $P = \frac{α}{β} \log_{e} (\frac{k t}{β x^{2}}) .$ Where $α$ and $β$ are constants, $x$ is distance, k is Boltzmann Constant and t is temperature. Then the dimensional formula of $α$ will be

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$[M^{0} L^{- 1} T^{0}]$

$[M^{1} L^{0} T^{- 2}]$

$[M^{1} L T^{- 2}]$

$[M^{1} L^{2} T^{- 2}]$

answer is B.

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Detailed Solution

$\frac{k t}{β x^{2}} = 1, β = \frac{k t}{x^{2}} = M^{1} T^{- 2}, P = \frac{α}{β}$

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