The angle of contact at the interface of water-glass is 0°, Ethylalcohol-glass is 0°, Mercury-glass is 140° an

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Q. The angle of contact at the interface of water-glass is 0°, Ethylalcohol-glass is 0°, Mercury-glass is 140° and Methyliodide-glass is 30°. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is

(a) water

(b) ethylalcohol

(d) methyliodide.

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Concept understanding — Capillary Action

Capillary Action: The Physics of Water Defying Gravity

You've seen it happen a hundred times. Dip the corner of a paper towel into a spill, and watch the water climb upward into the towel — against gravity. Or take a thin glass tube (a capillary), put it in water, and the water rises inside it, higher than the outside surface. That's capillary action.

The name comes from capillus, Latin for "hair" — because the effect is strongest in tubes as thin as a hair.

The Intuition: Two Forces at War

Think of water molecules as tiny magnets. They attract each other strongly (cohesion), and they also stick to the walls of a container (adhesion). In a narrow tube, adhesion to the glass pulls the water upward along the walls. The water molecules, clinging to each other, drag the entire column up with them.

But gravity pulls down. The water rises only until the upward pull from adhesion is exactly balanced by the weight of the water column. That's the equilibrium height.

Note

If adhesion is stronger than cohesion (water-glass), the liquid rises. If cohesion is stronger (mercury-glass), the liquid is depressed — it falls below the outside level. Mercury doesn't wet glass.

The Precise Physics: What Determines the Height?

For a liquid that wets the tube (contact angle $\theta < 90^\circ$ ), the rise height $h$ is given by the Jurin's law:

h = \frac{2\gamma \cos\theta}{\rho g r}

Where:

$\gamma$ = surface tension of the liquid (N/m)
$\theta$ = contact angle between liquid and tube wall
$\rho$ = density of the liquid (kg/m³)
$g$ = acceleration due to gravity (9.8 m/s²)
$r$ = radius of the tube (m)

h = \frac{2\gamma \cos\theta}{\rho g r}

The key insight: $h$ is inversely proportional to $r$ . Halve the tube radius, and the water rises twice as high. That's why the effect is only noticeable in very narrow tubes — in a wide pipe, $h$ is negligible.

Why Does Surface Tension Pull Upward?

The surface tension $\gamma$ acts along the circumference of the water-air interface inside the tube. The total upward force is:

F_{\text{up}} = (2\pi r) \times \gamma \cos\theta

The weight of the water column (height $h$ , density $\rho$ ) is:

F_{\text{down}} = (\pi r^2 h) \times \rho g

Set them equal, cancel $\pi r$ , and you get Jurin's law.

Tip

For water in clean glass, $\theta \approx 0^\circ$ (perfect wetting), so $\cos\theta = 1$ . Then $h \approx \frac{2\gamma}{\rho g r}$ . For water at room temperature, $\gamma \approx 0.073$ N/m, so $h \approx \frac{0.015}{r}$ (with $r$ in metres). A tube of radius 0.1 mm gives a rise of about 15 cm.

Real-World Examples

Paper towels and sponges: The fibres form millions of tiny capillary channels. Water rises through them, soaking the towel. …

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A convex meniscus forms when the angle of contact exceeds 90°, meaning the liquid does not wet the glass. Only mercury has $\theta = 140° > 90°$ , so the liquid is mercury.

The shape of the meniscus in a capillary tube is determined entirely by the angle of contact $\theta$ between the liquid and the solid surface. This angle measures how strongly the liquid molecules are attracted to the glass compared to each other.

When liquid molecules are more attracted to the glass than to themselves (strong adhesion), they climb up the walls and create a concave meniscus that curves upward at the edges. When liquid molecules prefer their own company (strong cohesion), they pull away from the glass and form a convex meniscus that bulges outward.

The critical threshold is $\theta = 90°$ :

$\theta < 90°$ : adhesion dominates → concave meniscus (liquid wets the glass)
$\theta > 90°$ : cohesion dominates → convex meniscus (liquid does not wet the glass)

Now let's examine each liquid:

Water-glass: $\theta = 0°$

This is perfect wetting. Water spreads completely on glass, forming a strongly concave meniscus. The capillary rise is maximum.
Ethyl alcohol-glass: $\theta = 0°$

Like water, ethyl alcohol wets glass completely. The meniscus is concave.
Mercury-glass: $\theta = 140°$

This angle is well above 90°. Mercury beads up on glass, refusing to wet it. The meniscus curves outward, forming a convex shape. Mercury also exhibits capillary depression (the liquid level inside the tube is lower than outside). …

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Q.The angle of contact at the interface of water-glass is 0°, Ethylalcohol-glass is 0°, Mercury-glass is 140° and Methyliodide-glass is 30°. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is

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