The graph between the mass of liquid inside the capillary and radius of capillary is

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Answer

To solve the problem of finding the relationship between the mass of liquid inside a capillary tube and the radius of the capillary, we can follow these steps:

### Step 1: Understand the Capillary Rise Formula
The height of capillary rise (H) is given by the formula:
\[ H = \frac{2S \cos \theta}{R \rho g} \]
where:
- \( S \) = surface tension of the liquid,
- \( \theta \) = angle of contact,
- \( R \) = radius of the capillary tube,
- \( \rho \) = density of the liquid,
- \( g \) = acceleration due to gravity.

### Step 2: Relate Height to Volume
The volume (V) of liquid that rises in the capillary can be expressed as:
\[ V = \pi R^2 H \]
where \( \pi R^2 \) is the cross-sectional area of the capillary tube.

### Step 3: Substitute Height in Volume Equation
Substituting the expression for \( H \) into the volume equation gives:
\[ V = \pi R^2 \left( \frac{2S \cos \theta}{R \rho g} \right) \]
This simplifies to:
\[ V = \frac{2S \pi R \cos \theta}{\rho g} \]

### Step 4: Relate Volume to Mass
The mass (m) of the liquid can be expressed as:
\[ m = \rho V \]
Substituting the expression for \( V \) gives:
\[ m = \rho \left( \frac{2S \pi R \cos \theta}{\rho g} \right) \]
This simplifies to:
\[ m = \frac{2S \pi \cos \theta}{g} R \]

### Step 5: Identify the Relationship
From the equation \( m = \frac{2S \pi \cos \theta}{g} R \), we can see that mass (m) is directly proportional to the radius (R):
\[ m \propto R \]

### Step 6: Graphical Representation
Since mass is directly proportional to radius, the graph of mass (m) versus radius (R) will be a straight line passing through the origin. This means that as the radius increases, the mass of the liquid inside the capillary also increases linearly.

### Final Conclusion
The graph between the mass of liquid inside the capillary and the radius of the capillary is a straight line passing through the origin.

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