ત્રણ પ્રવાહીની ઘનતાઓ \(\rho _1,\rho _2 \) અને \(\rho _3 (\rho _1 > \rho _2 > \rho _3)\) છે, તેમના પૃષ્ઠતાણ \(T\) ના મૂલ્યો સમાન છે, ત્રણ આદર્શ કેશનળીમાં ત્રણ પ્રવાહીઓ સમાન ઊંચાઇ સુધી ચઢે છે. સંપર્કકોણ \(\theta _1,\theta _2\) અને \(\theta _3\) શેનું પાલન કરે?

A \(\frac{\pi }{2} < {\theta _1} < {\theta _2} < {\theta _3} < \pi \;\)
B \(\;\pi > {\theta _1} > {\theta _2} > {\theta _3} > \frac{\pi }{2}\)
C \(\;\frac{\pi }{2} > {\theta _1} > {\theta _2} > {\theta _3} > 0\)
D \(\;0 \le {\theta _1} < {\theta _2} < {\theta _3} < \frac{\pi }{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\;0 \le {\theta _1} < {\theta _2} < {\theta _3} < \frac{\pi }{2}\)

Step-by-step Solution

Detailed explanation

\(Capillary\,rise,\,h = \frac{{2T\cos \theta }}{{r\rho g}}\) \(For\,given\,value\,of\,T\,and\,r,h \propto \frac{{\cos \theta }}{\rho }\)

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 NEET

Explore more questions on app