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

Answers (2)

Using the concepts we learnt:

 

Work, Potential Energy, Kinetic Energy, Torque -

\dpi{100} ML^{2}T^{-2}

 

- wherein

N-mt/Joule

 

 and

 

Momentum-Impulse -

MLT^{-1}

 

- wherein

kgms^{-1}

 

  and

 

Plank's Constant (h) -

M^{1}L^{2}T^{-1}

- wherein

Joule-sec

 

 

 


Option 1)

moment of inertia and moment of a force

Moment of Inertia \left ( I \right )= Mr^{2}

\therefore \; \; \; \; \left [ I \right ]= \left [ ML^{2} \right ]

Moment of force  rF= \left [ ML^{2} T^{-2}\right ]

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

 

Option 2)

work and torque

Work and Torque both have dimension \left [ ML^{2}T^{-2} \right ]

Option 3)

angular momentum and Planck’s constant

angular momentum and Planck’s constant  have dimension

\left [ angular\: momentum \right ]= \left [ ML^{2}T^{-1} \right ]

Also angular momentum= \frac{h}{2\pi }

\therefore 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.

N neha

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