The correct curve between the height or depression `h` of liquid in a capillary tube and its radius is

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the relationship between the height of liquid depression \( h \) in a capillary tube and its radius \( r \), we can follow these steps:

### Step 1: Understand Capillary Action
Capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. It occurs due to the adhesive and cohesive forces between the liquid and the solid surface of the tube.

### Step 2: Use the Capillary Rise Formula
The height of capillary rise (or depression) can be expressed using the formula:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
Where:
- \( h \) = height of the liquid column (capillary rise or depression)
- \( T \) = surface tension of the liquid
- \( \theta \) = contact angle
- \( \rho \) = density of the liquid
- \( g \) = acceleration due to gravity
- \( r \) = radius of the capillary tube

### Step 3: Analyze the Relationship
From the formula, we can see that \( h \) is inversely proportional to \( r \):
\[ h \propto \frac{1}{r} \]
This means that as the radius \( r \) of the capillary tube increases, the height \( h \) of the liquid column decreases.

### Step 4: Identify the Correct Curve
Since \( h \) is inversely proportional to \( r \), we can conclude that the relationship between \( h \) and \( r \) can be represented graphically as a hyperbola. Specifically, if you plot \( h \) against \( r \), you will get a curve that decreases as \( r \) increases.

### Conclusion
The correct curve between the height or depression \( h \) of the liquid in a capillary tube and its radius \( r \) is a hyperbolic curve, indicating that \( h \) decreases as \( r \) increases.

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