Applications of Dimensional Analysis question from JEE Main 2021 (31 Aug, Shift 1)

Answer: (a)

1. (a) Poiseuille's formula gives volume flow rate: $\frac{V}{t} = \frac{\pi p a^{4}}{8\eta L}$. Its RHS has dimensions $L^{3}T^{-1}$, not volume $L^{3}$, so it is incorrect.
2. (b) $\frac{s}{\rho r g} = \frac{MT^{-2}}{ML^{-3}\cdot L\cdot LT^{-2}} = L$: correct.
3. (c) $\epsilon \frac{\partial E}{\partial t}$ is displacement current density ($A\,m^{-2}$): correct.
4. (d) Work = torque × angle: correct.
5. So the answer is (a).