JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2021
- Hard
- MCQ
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.
Pick an option to check your answer.
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)
\((ii)\) \({h} \rho {g}=\frac{2 {s}}{{r}} \cos \theta\)
\((iii)\) \({RHS} \Rightarrow \varepsilon \times \frac{1}{4 \pi \varepsilon_{0}} \frac{{a}}{{r}^{2}} \times \frac{1}{\varepsilon}=\frac{{q}}{{t}} \times \frac{1}{{r}^{2}}\) \(=\frac{{I}}{{L}^{2}}={IL}^{-2}\)
\(LHS\)
\({T}=\frac{{I}}{{A}}={IL}^{-2}\)
\((iv)\) \({W}=\tau \theta\)
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