The unitless quantity is :

velocity gradient

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pressure gradiant

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displacement gradient

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force gradient

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Solution

The correct option is C displacement gradient
Velocity gradient $= \frac{d v}{d z} = \frac{L T^{- 1}}{L^{1}} = T^{- 1}$
Pressure gradient $= \frac{d p}{d z} = \frac{M^{1} L^{- 1} T^{- 2}}{L^{1}} = M^{1} L^{- 2} T^{- 2}$
Displacement gradient $= \frac{d z_{1}}{d z} = \frac{L^{1}}{L^{1}} = M^{0} L^{0} T^{0}$
Force gradient $= \frac{d f}{d z} = \frac{M^{1} L^{1} T^{- 2}}{L^{1}} = M T^{- 2}$
Hence, option C is correct.

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