Question

Which of the following pair does not have identical dimension ?

• A. Moment of inertia and moment of force
• B. Angular momentum and plank's constant
• C. Impulse and momentum
• D. Work and torque.

Answer 1

The correct option is B Angular momentum and plank's constant

Planck's constant, symbolized h, relates the energy in one quantum (photon) of electromagnetic radiation to the frequency of that radiation.

$h=\frac{E}{v}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[T^{-1}\right]}=\left[M{L}^2{T}^{-1}\right]$

Angular momentum $=$ Moment of inertia $\times$ Angular velocity (Angular momentum)

$=\left[M{L}^2\right]\left[T^{-1}\right]=\left[M{L}^2{T}^{-1}\right]$

So, here we can see that both the Planck's constant and Angular momentum have the same dimensions.