Looking for classes? Ksquare Career Institute, Bengaluru →
Which of the following equations is dimensionally incorrect? Where t = time, h = height, s = surface tension, $\theta$ = angle, $\rho$ = density, r = radius, $\xi$ = acceleration due to gravity, V = volume, P = pressure, W = work done, $\varepsilon$ = permittivity, E = electric field, J = current density, L = length, $\tau$ = torque
Explanation
(i) $\pi pa^{4}/(8\eta L) = dv/dt$ = Volumetric flow rate (Poiseuille's law) (ii) $\because h\rho g = (2s/r)\cos \theta \therefore h = 2s \cos \theta/(\rho rg)$ (iii) RHS $\Rightarrow \varepsilon \times (1/(4\pi\varepsilon_{0}))(a/r^{2}) \times (1/\varepsilon) = (q/t) \times (1/r^{2}) = 1/L^{2} = IL^{2}$. LHS $J = I/A = IL^{-2}$ (iv) $W = \tau\theta$.