\(0.015\;cm\) ત્રિજ્યા ધરાવતી કાંચની લાંબી કેશનળીને પ્રવાહીમાં ડૂબાડતા તેમાં પ્રવાહી \(15\, cm\) જેટલું ઉપર ચડે છે જો પ્રવાહીની સપાટી અને પાત્ર વચ્ચેનો સંપર્કકોણ \(0^{\circ}\) હોય તો પ્રવાહીનું પૃષ્ઠતાણ \(milli\,Newton \;m ^{-1}\) એકમમાં કેટલું હશે? [પ્રવાહીની ઘનતા \(\left.\rho_{\text {(liquid) }}=900\; kg\,m ^{-3}, g =10\, ms ^{-2}\right]\) (નજીકના પૂર્ણાંકમાં જવાબ આપો)

A \(115\)
B \(120\)
C \(101\)
D \(109\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(101\)

Step-by-step Solution

Detailed explanation

Capillary rise \(h =\frac{2 S \cos \theta}{\rho gr }\) \(S=\frac{\rho grh}{2 \cos \theta}\) \(=\frac{(900)(10)\left(15 \times 10^{-5}\right)\left(15 \times 10^{-2}\right)}{2}\) \(S=1012.5 \times 10^{-4}\) \(S=101.25 \times 10^{-3}=101.25 mN / m\) In question closest integer is…

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.

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