MHT CET · Physics · Mechanical Properties of Fluids

In a capillary tube having area of cross-section $A$ , the water rises to a height $h$ . If the cross-sectional area is reduced to $\frac{A}{9}$ , the rise of water in the capillary tube is

A $4 h$
B $3 h$
C $2 h$
D $h$

Verified Solution

Answer & Solution

Correct Answer

(B) $3 h$

Step-by-step Solution

Detailed explanation

A_{1} = π r_{1}^{2}

A_{2} = π r_{2}^{2}

\frac{π r_{1}^{2}}{9} = π r_{2}^{2}

\frac{r_{1}^{2}}{r_{2}^{2}} = 9 \Rightarrow \frac{r_{1}}{r_{2}} = 3

r h =

constant

r_{1} h_{1} = r_{2} h_{2}

\frac{r_{1}}{r_{2}} = \frac{h_{2}}{h_{1}}

3 = \frac{h_{2}}{h_{1}} = \frac{h_{2}}{h_{1}}

h_{2} = 3 h_{1} = 3 h

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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In a capillary tube having area of cross-section A, the water rises to a height h. If the cross-sectional area is reduced to A9, the rise of water in the capillary tube is

Step-by-step Solution

In a capillary tube having area of cross-section $A$ , the water rises to a height $h$ . If the cross-sectional area is reduced to $\frac{A}{9}$ , the rise of water in the capillary tube is