JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
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 \({W}=\Gamma \theta\)
Answer & Solution
Correct Answer
(A) \({v}=\frac{\pi {pa}^{4}}{8 \eta {L}}\)
Step-by-step Solution
Detailed explanation
\((i)\) \(\frac{\pi {pa}^{4}}{8 \eta {L}}=\frac{{d} {v}}{{dt}}=\) Volumetric flow rate (poiseuille's law) \((ii)\) \({h} \rho {g}=\frac{2 {s}}{{r}} \cos \theta\) \((iii)\)…
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