Question

The ratio of the dimensions of Planck constant and that of moment of inertia has the dimensions of:
A. angular momentum.B. time.C. velocity.D. frequency.

Answer 1

We know that the dimension of Planck constant = [M L^2 T^-1] and that of Moment of inertia = [M L^2 T^0] or [M L^2]

Now if we need to calculate its ratio we have to divide both the dimensions. After doing that we get,

[M L^2 T^-1]

----------------- = [T^-1] which is nothing but time inverse.

[M L^2 T^0]

We know that Frequency is number of complete cycles per second i.e. 1/T

Therefore [T^-1] is the dimension of Frequency.

Answer 2

Answer ⇒ Frequency

Explanation ⇒

S.I. unit of the Planks's constant is J-s.

∴ Dimensions of the Plank's constant = ML²T⁻² × T

= ML²T⁻¹

S.I. unit of the Moment of the Inertia = kg-m²

∴ Dimensions of the Moment of Inertia = ML²

∴ Ratio of the Dimensions of the Plank's constant and Moment of Inertia = ML²T⁻¹/ML²

= T⁻¹

Now, We know that [T⁻¹] is the Dimensions of the Frequency. Hence, Option (d). is correct.

Hope it helps. :-)