Which of the following equations is dimensionally incorrect? Where t= time, h= height, s= surface tension, theta= angle, rho= density, a, r= radius, g= acceleration

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

a $(i)$ $\frac{\pi {pa}^{4}}{8 \eta {L}}=\frac{{d} {v}}{{dt}}=$ Volumetric flow rate (poiseuille's law) $(ii)$ ${h} \rho {g}=\frac{2 {s}}{{r}} \cos \theta$ $(iii)$ ${RHS} \Rightarrow \varepsilon \times \frac{1}{4 \pi \varepsilon_{0}} \frac{{a}}{{r}^{2}} \times \frac{1}{\varepsilon}=\frac{{q}}{{t}} \times \frac{1}{{r}^{2}}$ $=\frac{{I}}{{L}^{2}}={IL}^{-2}$ $LHS$ ${T}=\frac{{I}}{{A}}={IL}^{-2}$ $(iv)$ ${W}=\tau \theta$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

Which of the following equations is dimensionally incorrect?

Where $t=$ time, $h=$ height, $s=$ surface tension, $\theta=$ angle, $\rho=$ density, $a, r=$ radius, $g=$ acceleration due to gravity, ${v}=$ volume, ${p}=$ pressure, ${W}=$ work done, $\Gamma=$ torque, $\varepsilon=$ permittivity, ${E}=$ electric field, ${J}=$ current density, ${L}=$ length.

A${v}=\frac{\pi {pa}^{4}}{8 \eta {L}}$
B${h}=\frac{2 {s} \cos \theta}{\rho {rg}}$
C${J}=\varepsilon \frac{\partial {E}}{\partial {t}}$
D${W}=\Gamma \theta$

JEE MAIN 2021, Diffcult

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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