What is the dimensional formula of work done by torque

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Solution

Dear Student,

Dimensional formula for work and torque are essentially the same.

$W o r k = \vec{F} . \vec{s} = F s \cos (θ) D i m e n s i o n o f F o r c e = M L T^{- 2} D i m e n s i o n o f s = L D i m e n s i o n o f W o r k = [M L T^{- 2}] [L] = [M L^{2} T^{- 2}]$

$T o r q u e = \vec{F} \times \vec{r} = F r \sin (θ) D i m e n s i o n o f F o r c e = M L T^{- 2} D i m e n s i o n o f r = L D i m e n s i o n o f T o r q u e = [M L T - 2] [L] = [M L^{2} T^{- 2}]$

$\frac{W o r k}{T o r q u e} = \frac{[M L^{2} T^{- 2}]}{[M L^{2} T^{- 2}]} = D i m e n s i o n l e s s q u a n t i t y$

Regards.

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