Question 142: Units , Dimensions and Error Analysis

Question

Which of the following equations is dimensionally incorrect?Where t = time, h = height, s = surface tension, $$	heta$$ = angle, $$ho$$ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T = torque, $$\in$$ = permittivity, E = electric field, J = current density, L = length.

Accepted Answer

(a) $${{\pi p{a^4}} \over {8\eta L}} = {{dv} \over {dt}}$$ = Volumetric flow rate (Poiseuille's law)
(b) $$hho g = {{2s} \over r}\cos 	heta $$
(c) $$\varepsilon  	imes {1 \over {4\pi {\varepsilon _0}}}{a \over {{r^2}}} 	imes {1 \over \varepsilon } = {q \over t} 	imes {1 \over {{r^2}}}$$
$$ = {1 \over {{L^2}}} = I{L^{ - 2}}$$
LHS
$$T = {I \over A} = I{L^{ - 2}}$$
(d) W = $$	au$$$$	heta$$
Option (a)

Answer

$$v = {{\pi p{a^4}} \over {8\eta L}}$$

Answer

$$h = {{2s\cos 	heta } \over {ho rg}}$$

Answer

$$J =  \in {{\partial E} \over {\partial t}}$$

Answer

$$W = \Gamma 	heta $$

Units , Dimensions and Error Analysis

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