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

Step-by-step solution

E=h h= Planck's constant = E [h]= [E] [ ] = [ ML ^2 ~T ⁻² ] [ T ⁻¹ ] = [ ML ^2 ~T ⁻¹ ] and I= moment of inertia =M R^2 Hence, [h] [I] = [ ML ^2 ~T ⁻¹ ] [ ML ^2 ] = [ T ⁻¹ ]= 1 [ ~T ] = dimensions of frequency Alternative: h I = E / I aligned & = E T I = ( kg - m ^2 / s ^2 ) s ( kg - m ^2 ) & = 1 s = 1 time = frequency aligned Thus, dimensions of h I is same as of frequency.