Which of the following equations is dimensionally incorrect?

Where t = time, h = height, s = surface tension, q = angle, p = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, $Γ$ = torque, = permittivity, $\in$ = electric field, J = current density, L = length.

Option 1 -

W = $Γ θ$

Option 2 -

$h = \frac{2 s c o s θ}{p r g}$

Option 3 -

$v = \frac{π p a^{4}}{8 η L}$

Option 4 -

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

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 3

Detailed Solution:

$\to [W] = [τ θ] = [M L^{2} T^{- 2}] \to c o r r e c t$

$\to [h] = [L] = [\frac{2 s c o s θ}{ρ r g}] \to c o r r e c t$

$[v] = [L^{3}] [\frac{π p a^{4}}{8 η L}] = [L^{3} T^{- 1}] \to$ Incorrect

$\to J = ε \frac{\partial E}{\partial t} \to$ correct

$[A \overset{↓}{L}^{- 2}] [A \overset{↓}{L}^{- 2}]$

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