Which one of the following is a dimensionless | vedclass

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(A) physical quantity is dimensionless if it has no dimensions in terms of mass $(M)$,length $(L)$,and time $(T)$. $1$. Angle is defined as the ratio

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Angle

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(A) physical quantity is dimensionless if it has no dimensions in terms of mass $(M)$,length $(L)$,and time $(T)$. $1$. Angle is defined as the ratio of arc length to radius,i.e.,$	heta = \frac{s}{r}$. Since both are lengths,the dimensions are $[L]/[L] = [M^0 L^0 T^0]$,making it dimensionless. $2$. Stress is defined as force per unit area,$[M L T^{-2}] / [L^2] = [M L^{-1} T^{-2}]$. $3$. Force gradient is force per unit length,$[M L T^{-2}] / [L] = [M T^{-2}]$. $4$. Velocity gradient is velocity per unit length,$[L T^{-1}] / [L] = [T^{-1}]$. Therefore,Angle is the correct answer.

Which one of the following is a dimensionless physical quantity?

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