Two capillary tubes of radii 0.2 cm and 0.4 cm are dipped in the same liquid. The ratio of hei

step 1 The given data of this question is in this question there is two capillary tubes A and B, which

Two capillary tubes of radii 0.2 cm and 0.4 cm are dipped...

Two capillary tubes of radii $0.2 \mathrm{~cm}$ and $0.4 \mathrm{~cm}$ are dipped in the same liquid. The ratio of heights through which liquid will rise in the tubes is
(a) $1: 2$
(b) $2: 1$
(c) $1: 4$
(d) $4: 1$

Key Concepts

Inverse Proportionality

In the context of capillary action, the inverse proportionality refers to the relationship where the height to which the liquid rises is inversely proportional to the radius of the tube. This means that as the radius increases, the height of the liquid column decreases, a principle that is key to understanding how liquid behavior varies in capillary tubes of different diameters.

Capillary Rise Equation

The capillary rise equation, commonly given as h = (2T cos?)/(?g r), relates the height (h) to which a liquid will rise in a capillary tube to the surface tension (T), the contact angle (?), the density of the liquid (?), gravitational acceleration (g), and the radius of the tube (r). This equation shows that the height is inversely proportional to the tube's radius, meaning narrower tubes result in a higher rise.

Capillary Action

Capillary action is the phenomenon by which a liquid rises or falls in a narrow tube due to the intermolecular forces between the liquid and the tube material. This rise or depression occurs because the adhesive forces between the liquid and the walls of the tube, combined with the liquid's surface tension, work against gravity.

Surface Tension

Surface tension is the force per unit length existing at the interface between a liquid and a gas or between two immiscible liquids. It is responsible for minimizing the surface area of the liquid and plays a crucial role in capillary action by influencing the curvature of the liquid meniscus that forms inside the tube.

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