When a glass capillary tube of radius 0.015 cm is dipped in water, the water rises to a height

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When a glass capillary tube of radius 0.015 cm is dipped in...

When a glass capillary tube of radius $0.015 \mathrm{~cm}$ is dipped in water, the water rises to a height of $15 \mathrm{~cm}$ within it. Assuming contact angle between water and glass to be $0^{\circ}$, the surface tension of water is $\left[\rho_{\text {water }}=1000 \mathrm{~kg} \mathrm{~m}^{-3,} \mathrm{~g}=9.81 \mathrm{~ms}^{-2}\right]$ (a) $0.11 \mathrm{Nm}^{-1}$ (b) $0.7 \mathrm{Nm}^{-1}$ (c) $0.072 \mathrm{Nm}^{-1}$ (d) None of the above

When a glass capillary tube of radius $0.015 \mathrm{~cm}$ is dipped in water, the water rises to a height of $15 \mathrm{~cm}$ within it. Assuming contact angle between water and glass to be $0^{\circ}$, the surface tension of water is $\left[\rho_{\text {water }}=1000 \mathrm{~kg} \mathrm{~m}^{-3,} \mathrm{~g}=9.81 \mathrm{~ms}^{-2}\right]$
(a) $0.11 \mathrm{Nm}^{-1}$
(b) $0.7 \mathrm{Nm}^{-1}$
(c) $0.072 \mathrm{Nm}^{-1}$
(d) None of the above

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Key Concepts

Hydrostatic Equilibrium

Hydrostatic equilibrium in the context of capillarity refers to the balance between the upward force due to surface tension along the tube wall and the downward gravitational force on the liquid column. This balance determines the height to which the liquid rises in the tube.

Contact Angle

The contact angle is the angle formed between the tangent to the liquid surface at the point of contact and the solid surface. It is critical in capillary phenomena because it affects the adhesion between the liquid and the solid, with smaller contact angles (indicating better wetting) leading to a greater capillary rise.

Surface Tension

Surface tension is the cohesive force at a liquid's surface that causes the surface to contract and resist external force. It is a key parameter in capillarity as it determines the magnitude of the upward force acting along the liquid interface in a capillary tube.

Capillary Action

Capillary action is the phenomenon where a liquid rises or falls in a narrow tube due to the cohesive forces within the liquid and the adhesive forces between the liquid and the tube material. It is a classic example of the interplay between surface tension and gravitational forces, which can be quantified using the capillary rise formula.

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