Question

Which of the following quantity is unitiess?
(1) Velocity gradient (2) Pressure gradient
(3) Displacement gradient (4) Force gradient
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Answer 1

Answer:

Displacement Gradient

Explanation:

Gradient of a quantity Q is given as

∆Q /∆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.

Answer 2

Answer:

SI unit of Velocity Gradient is s-1.

SI unit of Pressure gradient is (Pa/m).

SI unit of Force gradient is (N/m).

Hence Displacement gradient is a unit-less quantity.