# Out of the following pairs which one does not have identical dimensions is Option 1) moment of inertia and moment of a force Option 2) work and torque Option 3) angular momentum and Planck’s constant Option 4) impulse and momentum

Using the concepts we learnt:

Work, Potential Energy, Kinetic Energy, Torque -

- wherein

and

Momentum-Impulse -

- wherein

and

Plank's Constant (h) -

- wherein

Joule-sec

Option 1)

moment of inertia and moment of a force

Moment of Inertia

Moment of force

Hence moment of inertia & moment of force does not have same dimension.

Option 2)

work and torque

Work and Torque both have dimension

Option 3)

angular momentum and Planck’s constant

angular momentum and Planck’s constant  have dimension

Also angular momentum

Dimension of Planck’s constant is same as angular momentum.

Option 4)

impulse and momentum

Impulse is change in momentum hence both have same dimensions.

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