The efficiency of an engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \cdot \log _{\mathrm{e}} \frac{\beta \mathrm{x}}{\mathrm{kT}}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is the absolute temperature, \(k\) - Boltzmann constant, \(\theta\)-angular displacement and \(\mathbf{x}\) is distance, then the incorrect statement is

1. A Dimensions of \(\beta\) are same as that of force
2. B Dimensions of \(\alpha^{-1} \mathrm{x}\) are same as that of energy
3. C Dimensions of \(\eta^{-1} \sin \theta\) are same as that of \(\alpha \beta\)
4. D Dimensions of \(\alpha\) are same as that of \(\beta\)