Question

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

​

Answer 1

Which of the following quantity is unitless?

(1) Velocity gradient

(2) Pressure gradient

(3) Displacement gradient

(4) Force gradient

3) Displacement gradient

Gradient is referred yo as per unit length.

Displacement gradient is length per unit length.

Hence it is unitless quantity.

hope it helps.

Answer 2

Answer:

Displacement gradient is unitless quantity i.e.option(3).

Explanation:

Let's analyze the options one by one,

(1) Velocity gradient(Vg)-the velocity of a liquid crossing per unit meter of a tube. It is given as,

$V_g=\frac{V}{x}=\frac{m/s}{m}=s^-^1$          (a)

(2)Pressure gradient(Pg)-It is a way to describe the difference in atmospheric pressure from one location to another.

$P_x=\frac{P}{x}=\frac{kg\times m^-^1\times s^-^2}{m}=kgm^-^2s^-^2$       (b)

(3)Displacement gradient-the gradients of displacement fields are called displacement gradients.

$X_x=\frac{x}{x}=\frac{m}{m}=1$                (c)

(4)Force gradient-it is defined as the force acting per unit meter over a specified area. It is given as,

$F_x=\frac{F}{x}=\frac{kg\times m s^-^2}{m}=kg s^-^2$

Hence after studying the options one by one we get to know that only displacement gradient is unitless i.e.option(3).