The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

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1. **Planck's Constant ($h$):** According to Planck's quantum theory, energy is given by $E = h
u$ . Thus, the dimensions of Planck's constant are $\frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}]$ .
2. **Moment of Inertia ($I$):** The formula for moment of inertia is $I = \sum mr^2$ . Its dimensions are $[M][L^2] = [ML^2]$ .
3. **Ratio:** Taking the ratio of their dimensions, we get $\frac{[h]}{[I]} = \frac{[ML^2T^{-1}]}{[ML^2]} = [T^{-1}]$.
4. **Conclusion:** The resulting dimension $[T^{-1}]$ is the dimensional formula for frequency .

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