Physics - Unit & Dimension Question with Solution | TestHub

In given equation,$\frac{az}{k\mathrm{\theta }}$should be dimensionless

$\alpha =\frac{k\mathrm{\theta }}{z}$

$\Rightarrow \left[\alpha \right]=\frac{\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}\times \mathrm{K}\right]}{\left[\mathrm{L}\right]}=\left[\mathrm{M}\mathrm{L}{\mathrm{T}}^{-2}\right]$

And$p=\frac{\alpha }{\beta }$

$\Rightarrow \left[\mathrm{\beta }\right]=\left[\frac{\alpha }{p}\right]=\frac{\left[\mathrm{M}\mathrm{L}{\mathrm{T}}^{-2}\right]}{\left[\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}\right]}=\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^0\right]$