નીચે પૈકી કયું સમીકરણ પારિમાણિક રીતે ખોટું થાય? જ્યાં \(t=\)સમય, \(h=\)ઊંચાઈ, \(s=\)પૃષ્ઠતાણ, \(\theta=\)ખૂણો, \(\rho=\)ઘનતા, \(a, r=\)ત્રિજ્યા, \(g=\)ગુરુત્વ પ્રવેગ, \({v}=\)કદ, \({p}=\)દબાણ, \({W}=\)કાર્ય, \(\Gamma=\)ટોર્ક, \(\varepsilon=\)પરમિટિવિટી, \({E}=\)વિદ્યુતક્ષેત્ર, \({J}=\)પ્રવાહઘનતા, \({L}=\)લંબાઈ

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 \({W}=\Gamma \theta\)

Verified Solution

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) \((ii)\) \({h} \rho {g}=\frac{2 {s}}{{r}} \cos \theta\) \((iii)\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From JEE Mains

Explore more questions on app