Question

Out of the following the only pair that does not have identical dimensions is:
1. angular momentum and Planck's constant
2. moment of inertia and moment of a force
3. work and torque
4. impulse and momentum

Answer 1

Correct Answer - Option 2 : moment of inertia and moment of a force

CONCEPT:

Dimensions

• Dimensions of a physical quantity are the powers to which the fundamental units are raised to obtain one unit of that quantity.

​EXPLANATION:

Physical quantity	Dimension
Angular momentum	\(\left [ M^{1}L^{2}T^{-1} \right ]\)
Planck's constant	\(\left [ M^{1}L^{2}T^{-1} \right ]\)
Moment of inertia	\(\left [ M^{1}L^{2}T^{0} \right ]\)
Moment of force	\(\left [ M^{1}L^{2}T^{-2} \right ]\)
Work	\(\left [ M^{1}L^{2}T^{-2} \right ]\)
Torque	\(\left [ M^{1}L^{2}T^{-2} \right ]\)
Impulse	\(\left [ M^{1}L^{1}T^{-1} \right ]\)
Momentum	\(\left [ M^{1}L^{1}T^{-1} \right ]\)

• From the above table, it is clear that the moment of inertia and moment of a force does not have the same dimensions. Hence, option 2 is correct.