The ratio of the dimensions of Planck constant and that of moment of inertia is the dimensions of

To find the physical quantity corresponding to the ratio of the dimensions of Planck's constant to the dimensions of the moment of inertia, we first determine the dimensions of each quantity individually.

1. Dimensions of Planck's constant ($h$):
The energy of a photon is given by the relation:
$E=h\nu$
where $E$ is energy and $\nu$ is frequency.
Since frequency $\nu =\frac{1}{T}$, its dimension is:
$\left[\nu \right]=\left[T^{-1}\right]$
The dimensions of energy $E$ are:
$\left[E\right]=\left[M{L}^2{T}^{-2}\right]$
Therefore, the dimensions of Planck's constant $h$ are:
$\left[h\right]=\frac{\left[E\right]}{\left[\nu \right]}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[T^{-1}\right]}$

2. Dimensions of Moment of Inertia ($I$):
The moment of inertia of a body is defined as:
$I=m{r}^2$
where $m$ is mass and $r$ is distance.
Thus, the dimensions of the moment of inertia $I$ are:
$\left[I\right]=\left[M{L}^2\right]$

3. Ratio of the dimensions:
Now, we find the ratio of the dimensions of Planck's constant to the moment of inertia:
$\frac{\left[h\right]}{\left[I\right]}=\frac{\left[M{L}^2{T}^{-1}\right]}{\left[M{L}^2\right]}=\left[T^{-1}\right]$

The dimension $\left[T^{-1}\right]$ represents frequency.

Therefore, the correct option is frequency.