MHT CET · Physics · Mechanical Properties of Fluids

A capillary tube is vertically immersed in water, water rises upto a height 'h \(_{1}\) '. When
the whole arrangement is taken to a depth 'd' in a mine, the water level rises upto
height \({ }^{\prime} h_{2}\) '. The ratio \(\mathrm{h}_{1} / \mathrm{h}_{2}\) is
\((\mathrm{R}=\) radius of earth \()\)

A \(\left(1+\frac{2 \mathrm{~d}}{\mathrm{R}}\right)\)
B \(\left(1-\frac{d}{R}\right)\)
C \(\left(1+\frac{\mathrm{d}}{\mathrm{R}}\right)\)
D \(\left(1-\frac{2 d}{R}\right)\)

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Answer & Solution

Correct Answer

(B) \(\left(1-\frac{d}{R}\right)\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & h=\frac{2 T \cos \theta}{r \rho g} \\ \therefore & h \alpha \frac{1}{g} \\ \therefore & \frac{h_{1}}{h_{2}}=\frac{g_{2}}{g_{1}}=1-\frac{d}{R} \end{aligned}\)

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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A capillary tube is vertically immersed in water, water rises upto a height 'h \(_{1}\) '. Whenthe whole arrangement is taken to a depth 'd' in a mine, the water level rises uptoheight \({ }^{\prime} h_{2}\) '. The ratio \(\mathrm{h}_{1} / \mathrm{h}_{2}\) is\((\mathrm{R}=\) radius of earth \()\)

Step-by-step Solution