On putting a capillary tube in a pot filled with water, the...

On putting a capillary tube in a pot filled with water, the level of water rises up to a height of $4 \mathrm{~cm}$ in the tube. If a tube of half the diameter is used, the water will rise to the height of nearly (A) $2 \mathrm{~cm}$ (B) $5 \mathrm{~cm}$ (C) $8 \mathrm{~cm}$ (D) $11 \mathrm{~cm}$

On putting a capillary tube in a pot filled with water, the level of water rises up to a height of $4 \mathrm{~cm}$ in the tube. If a tube of half the diameter is used, the water will rise to the height of nearly
(A) $2 \mathrm{~cm}$
(B) $5 \mathrm{~cm}$
(C) $8 \mathrm{~cm}$
(D) $11 \mathrm{~cm}$

Key Concepts

Tube Diameter's Influence on Capillary Rise

The relationship between the tube diameter and the height of the liquid rise is a key concept in understanding capillary action. As the diameter decreases, the height of the liquid column increases, assuming other factors remain constant. This inverse dependency is critical in predicting changes in capillary action when the dimensions of the tube are altered.

Capillary Rise Equation

The capillary rise in a tube is quantitatively described by an equation that relates the height of the liquid column to the surface tension, the contact angle, the density of the liquid, gravitational acceleration, and the tube's radius. This equation shows that the height of the capillary rise is inversely proportional to the diameter of the tube.

Capillary Action

Capillary action is the phenomenon where a liquid rises or falls in a narrow tube due to the balance between cohesive forces within the liquid and adhesive forces between the liquid and the tube material. This effect is most noticeable in small diameter tubes, where surface tension plays a significant role in counteracting gravity.

Surface Tension

Surface tension is the property of a liquid's surface that allows it to resist external forces, owing to the cohesive forces among its molecules. In the context of capillary action, surface tension causes the liquid to climb up the walls of a narrow tube, forming a meniscus and leading to a rise in the liquid level.

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