MCQ
Which of the following is unitless quantity ?
- AVelocity gradient
- BPressure gradient
- ✓Displacement gradient
- DForce gradient
✓
Answer
Correct option: C.
Displacement gradient
c
Gradient of a quantity $Q$ is given as $\frac{\Delta Q}{\Delta x}$
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.
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