Question

Which donot have same dimensions. 1. Work and energy 2. Work and torque 3. Momentum and impulse 4. Mass and moment of inertia

Answer 1

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.

Answer 2

I can notgive your answers

sorry