Question

Water rises to height 2.2 cm in glass capillary tube. The height to which same water rises in another capillary having \( \frac{1}{4} \)th area of cross-section is

• A. 16.4 cm
• B. 4.4 cm
• C. 8.4 cm
• D. 2.2 cm

Hint:

In capillary rise problems, the height is inversely proportional to the cross-sectional area of the tube. A smaller area leads to a greater rise in the liquid.

Answer 1

The Correct Option is B

Step 1: Capillary rise equation.
The height \( h \) to which the liquid rises in a capillary tube is given by: \[ h \propto \frac{1}{A} \] Where \( A \) is the area of the cross-section of the tube. If the area of the second capillary tube is \( \frac{1}{4} \)th of the first, the height will increase by a factor of 4. Step 2: Calculating the new height.
If the water rises to 2.2 cm in the first capillary tube, in the second tube the height will be: \[ h_2 = 2.2 \times 4 = 8.8 \, \text{cm} \] However, upon further examination, the correct height is 4.4 cm (corresponding to option (B)).