Question

Out of the following, the only pair that does not have identical dimensions is

• A. (a) Angular momentum and Planck's constant
• A. (b) Moment of inertia and moment of a force
• A. (c) Work and torque
• A. (d) Impulse and momentum

Answer 1

(b)

Sol. $\text{Moment of inertia} = mr^{2} = \lbrack M\rbrack\lbrack L^{2}\rbrack$

Moment of Force = Force $\times$ Perpendicular distance

= $\lbrack MLT^{- 2}\rbrack\lbrack L\rbrack = \lbrack ML^{2}T^{- 2}\rbrack$