Question

Ratio of dimensions of planck's constant and that of moment of inertia is dimension of

Answer 1

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

= ML²T⁻¹

Dimensions of Moment of Inertia = ML²T°

∴ Ratio = ML²T⁻¹/ML²T°

= T⁻¹

which is the dimension of frequency.

Hope it helps.

Answer 2

Answer: The correct answer is frequency.

Explanation:

The expression for the energy in terms of Planck's constant and frequency is as follows:

E=hf

Here, h is Planck's constant and f is the frequency.

The dimension of the frequency is $T^{-2}$

Then, the dimension of the Planck's constant is as follows;

$h=\frac{E}{f}$

Dimensions of the Plank's constant =$ML^{2}T^{-2}(T)$

Dimensions of the Plank's constant = $ML^{2}T^{-1}$

The expression for the moment of inertia is as follows;

$I=Mr^{2}$

Dimensions of Moment of Inertia = $=ML^{2}$

Calculate the ratio of the  dimensions of planck's constant and that of moment of inertia.

Ratio=$\dfrac{ML^2T^{-1}}{ML^2}$

Ratio=$T^{-1}$

 It is the dimension of frequency.

Therefore, the answer is frequency.