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Water rises to a height of 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary tube having half of the cross-sectional area.

Answer :

Final answer:

Capillary action refers to a fluid's ability to flow in narrow spaces without assistance from external forces. The height to which water will rise in a capillary tube with half the cross-sectional area compared to another tube is inversely proportional to the square root of the radius change. The new height will be approximately 4.52 cm.

Explanation:

The question involves the concept of capillary action, which is a physical phenomenon observed when a liquid rises or falls in a narrow space such as a thin tube, due to the forces of adhesion, cohesion, and surface tension.

In this case, we need to calculate the height to which water will rise in a glass capillary tube with half of the cross-sectional area compared to another tube in which water rises to a height of 3.2 cm.

According to the principles of capillary action, the height to which a liquid rises is inversely proportional to the radius (and thus the cross-sectional area) of the capillary tube.

If the cross-sectional area of the second capillary tube is half that of the first, then the radius of the second tube is √(1/2) times that of the first, due to the area being proportional to the square of the radius.

Since the height is inversely proportional to the radius, the water will rise to a height of √2 or approximately 1.414 times higher in the second tube.

So, the new height will be 3.2 cm * 1.414, which equals approximately 4.52 cm.

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