If the capillary rise of water in a 2 mm diameter tube is 1.5 cm, the height of capillary rise in a 0.5 mm diameter tube, in cm, will be

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BPSC AE Paper V Mechanical 2024 Official Paper

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Answer 1

Explanation:

Capillary Rise:

Capillary rise refers to the phenomenon where a liquid rises or falls in a narrow tube due to the combined effects of surface tension and adhesion between the liquid and the tube material. This behavior is a consequence of the liquid's cohesive and adhesive forces, and it is most commonly observed in liquids like water.

The height of capillary rise is inversely proportional to the diameter of the tube:

\( h \propto \frac{1}{d} \Rightarrow \frac{h_1}{h_2} = \frac{d_2}{d_1} \Rightarrow h_2 = h_1 \cdot \frac{d_1}{d_2} \)

Calculation:

Given:

Capillary rise in 2 mm tube, \( h_1 = 1.5~\text{cm} \)

Diameters: \( d_1 = 2~\text{mm},~d_2 = 0.5~\text{mm} \)

Now,

\( h_2 = 1.5 \cdot \frac{2}{0.5} = 1.5 \cdot 4 = 6.0~\text{cm} \)