1. Tardigrade
  2. Question
  3. Physics
  4. Which of the following equations is dimensionally incorrect? Where t = time, h = height, s = surface tension, θ= angle,ρ= density , a , r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, Gamma= torque, ∈= permittivity, E = electric field, J = current density, L = length

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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, $\in=$ permittivity, $E =$ electric field, $J =$ current density, $L =$ length

JEE MainJEE Main 2021Physical World, Units and Measurements

Solution:

(i) $\frac{\pi pa ^{4}}{8 \eta L }=\frac{ dv }{ dt }$
$=$ 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) $W =\tau \theta$