When a long glass capillary tube of radius \(0.015\;cm\) is dipped in a liquid, the liquid rises to a height of \(15\, cm\) within it. If the contact angle between the liquid and glass to clase to \(0^{\circ},\) the surface tension of the liquid, in \(milli\,Newton \;m ^{-1}\) is \(.....\) \(\left[\rho_{\text {(liquid) }}=900\; kg\,m ^{-3}, g =10\, ms ^{-2}\right]\) (Give answer in closest integer)

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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Match List \(I\) with List \(II\).

LIST \(-I\)	LIST \(-II\)
\((A)\) Torque	\((I)\) \(kg\,m ^{-1}\,s ^{-2}\)
\((B)\) Energy density	\((II)\) \(kg\,m\,s^{-1}\)
\((C)\) Pressure gradient	\((III)\) \(kg\,m ^{-2}\,s ^{-2}\)
\((D)\) Impulse	\((IV)\) \(kg\,m ^2\,s ^{-2}\)

Choose the correct answer from the options given below

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