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The ratio of the dimension of Planck's constant and that of the moment of inertia is the dimension of :
A
Velocity
B
Angular momentum
C
Time
D
Frequency
Detailed Solution
Planck's constant $h = \dfrac{E}{\nu}$, so its unit is J s: $[h] = [ML^2T^{-2}][T] = [ML^2T^{-1}]$
Moment of inertia $I = mr^2$, with unit kg m$^2$: $[I] = [ML^2]$
$\dfrac{[h]}{[I]} = \dfrac{ML^2T^{-1}}{ML^2}$
$= [T^{-1}]$
$[T^{-1}]$ is the dimension of frequency (also of angular velocity).
So the ratio has the dimension of frequency.
Moment of inertia $I = mr^2$, with unit kg m$^2$: $[I] = [ML^2]$
$\dfrac{[h]}{[I]} = \dfrac{ML^2T^{-1}}{ML^2}$
$= [T^{-1}]$
$[T^{-1}]$ is the dimension of frequency (also of angular velocity).
So the ratio has the dimension of frequency.