Question:
Two capillary tubes A and B of diameter 1 mm and 2 mm respectively are dipped vertically in a liquid. If the capillary rise in A is 6 cm, then the capillary rise in B is
Two capillary tubes A and B of diameter 1 mm and 2 mm respectively are dipped vertically in a liquid. If the capillary rise in A is 6 cm, then the capillary rise in B is
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Capillary rise is inversely proportional to tube radius or diameter.
Updated On: May 8, 2026
- 2 cm
- 3 cm
- 4 cm
- 6 cm
- 9 cm
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The Correct Option is B
Solution and Explanation
Concept:
Capillary rise is given by:
\[
h = \frac{2T \cos \theta}{\rho g r}
\]
Since all quantities except radius are constant:
\[
h \propto \frac{1}{r} \propto \frac{1}{d}
\]
Step 1: Establish proportionality. \[ \frac{h_1}{h_2} = \frac{d_2}{d_1} \]
Step 2: Substitute given values. \[ \frac{6}{h_2} = \frac{2}{1} \]
Step 3: Solve for \(h_2\). \[ h_2 = \frac{6}{2} = 3 \, \text{cm} \]
Step 4: Conclusion. \[ \boxed{3 \, \text{cm}} \]
Step 1: Establish proportionality. \[ \frac{h_1}{h_2} = \frac{d_2}{d_1} \]
Step 2: Substitute given values. \[ \frac{6}{h_2} = \frac{2}{1} \]
Step 3: Solve for \(h_2\). \[ h_2 = \frac{6}{2} = 3 \, \text{cm} \]
Step 4: Conclusion. \[ \boxed{3 \, \text{cm}} \]
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