Question

Which of the following quantity is unitless ?

• A. Velocity gradient
• B. Pressure gradient
• C. Displacement gradient
• D. Force gradient

Answer 1

Answer: (C)

Displacement gradient

Gradient of a quantity $Q$ is given as $\frac{\Delta Q}{\Delta x}$
Thus, a gradient will be unitless if its numerator has same dimensions as denominator, i.e. $x$ (which has the dimension $L$).
Thus, out of the options, Displacement has the dimension $L$ and hence its gradient will be dimensionless.