Identify the pair whose dimensions are equal.

Option 1)

torque and work

Option 2)

stress and energy

Option 3)

force and stress

Option 4)

force and work.

Answers (2)

Torque and work have the same dimensions .

Using as we learnt in:

Work, Potential Energy, Kinetic Energy, Torque -

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

 

- wherein

N-mt/Joule

 

 

 


Option 1)

torque and work

torque and work

Torque  \vec{\tau }= \vec{r}\times \vec{f}

Work w= \vec{f}\times \vec{r}

( Hence both are product of \vec{r} and \vec{f} and hence both has same dimension).

Option 2)

stress and energy

stress and energy

Stress = \frac{force}{area} and energy is product of force and displacement.

Hence Energy and stress have different dimension.

Option 3)

force and stress

force and stress

Stress = \frac{force}{area}

Hence dimension of stress is different from force.

Option 4)

force and work.

force and work.

Work - Force \times displacement

Hence dimension of force and work are different .

 

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