Question

From the following pairs, choose the pair that does not have identical dimensions ?

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

Answer 1

Answer: (C)

Moment of inertia and moment of force

Impulse is change in momentum ($p_2-p_1$).

Thus, they have same dimensions.
Work is dot product of Force and displacement while Torque is the cross product of Force and radius vector.

Thus they have same dimensions (of Fr = $ML{T}^{-2}\times L=M{L}^2{T}^{-2}$)
Angular moment and Planck's constant also have the same dimensions because Angular moment = Momentum $\times$ length. Planck's constant is Momentum $\times$ Wavelength (because $p=\frac{h}{\lambda }$)
Thus they have same dimensions.
Moment of Inertia has dimensions $M{L}^2$ and moment of force, i.e. Torque has dimensions $M{L}^2{T}^{-2}$, thus different.