Find the dimensional formula of the ratio of Planck's constant and the moment of inertia. 

According to Planck :

$\begin{array}{l}\mathrm{E}=\mathrm{hv}\\ \text{ or }\mathrm{h}=\frac{\mathrm{E}}{\mathrm{v}}\end{array}$

Substituting the dimensions of known physical quantities :

$\begin{array}{c}\left[\mathrm{h}\right]=\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{T}}^{-1}\right]}\\ \text{ or }\left[\mathrm{h}\right]={\mathrm{ML}}^2{\mathrm{T}}^{-1}\end{array}$

Now, we know that moment of inertia, I -

$\begin{array}{l}\mathrm{I}=\sum {\mathrm{mr}}^2\\ \therefore \left[\mathrm{I}\right]=\left[{\mathrm{ML}}^2\right]\\ \therefore \text{ ratio, }\frac{\mathrm{h}}{\mathrm{I}}=\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]}{\left[{\mathrm{ML}}^2\right]}={\mathrm{T}}^{-1}\end{array}$

i.e. it has the dimensions of frequency.