Given that, η=sinθαβlog(kTβx). Since expression inside the logarithm is dimensionless
[βx]=[kT]
Since the dimensions of kT are equivalent to that of energy,
[β]=[x][kT]=[x][E]=[L][ML2T−2]=[MLT−2]
Therefore, β has dimensions of force.
Since efficiency is a dimensionless ratio,
[α][β]=[M0L0T0]
⇒[β]=[α]1
Therefore, dimensions of α is not same as that of β. Hence option D is incorrect statement and the answer.
[α][x]=[β][x]=[ML2T−2]. Therefore, α−1x has dimensions of energy.