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Question:

Which of the following pairs does not have the same dimensions?

impulse and momentum

moment of inertia and moment of force

angular momentum and Planck's constant

work and torque

Solution:

Moment of force (τ) is equal to the product of moment of inertia (I) and the angular acceleration (α) of the rotating body.
∴ τ = Iα
Hence the dimensions of moment of force and moment of inertia must be different.