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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

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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.

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