Q. Out of the following pairs, which one does not have identical dimensions?
A) Angular momentum and Planck’s constant
B) Impulse and momentum
C) Moment of inertia and moment of a force
D) Work and torque
Explanation
Moment of inertia $I = mr^{2}$ $\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack I\rbrack = \left\lbrack ML^{2} \right\rbrack$ And $\tau = moment\ of\ force = \mathbf{r \times F}$ $\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack\tau\rbrack = \lbrack L\rbrack\left\lbrack MLT^{- 2} \right\rbrack = \left\lbrack ML^{2}T^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.