Which of the following is a unitless quantity | vedclass

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(C) The gradient of a physical quantity $Q$ is defined as the rate of change of that quantity with respect to distance,given by $\frac{dQ}{dx}$.For a

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Displacement gradient

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(C) The gradient of a physical quantity $Q$ is defined as the rate of change of that quantity with respect to distance,given by $\frac{dQ}{dx}$.For a gradient to be unitless,the dimensions of the numerator $Q$ must be the same as the dimensions of the denominator $x$ (which is length,$L$).$1$. Velocity gradient: $\frac{[LT^{-1}]}{[L]} = [T^{-1}]$,which has units of $s^{-1}$.$2$. Pressure gradient: $\frac{[ML^{-1}T^{-2}]}{[L]} = [ML^{-2}T^{-2}]$,which has units of $Pa/m$.$3$. Displacement gradient: $\frac{[L]}{[L]} = [M^0L^0T^0]$,which is dimensionless and unitless.$4$. Force gradient: $\frac{[MLT^{-2}]}{[L]} = [MT^{-2}]$,which has units of $N/m$.Therefore,the displacement gradient is the unitless quantity.

Which of the following is a unitless quantity?

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