A false statement is

Options

A. Angle of contact `theta lt 90^(@)`, if cohesive force `lt` adhesive force
B. Angle of contact `theta gt 90^(@)`, if cohesive force `gt` adhesive force
C. Angle of contact `theta = 90^(@)`, if cohesive force = adhesive force
D. If the radius of capillary is reduced to half, the rise of liquid column becomes four times

Answer

To determine which statement is false regarding surface tension and capillarity, let's analyze each statement step by step.

### Step 1: Analyze the First Statement
- **Statement**: The angle of contact is less than 90 degrees, so the adhesive force is less than the cohesive force.
- **Analysis**: This statement is true. When the angle of contact is less than 90 degrees, it indicates that the adhesive forces (between the liquid and the solid) are stronger than the cohesive forces (within the liquid).

### Step 2: Analyze the Second Statement
- **Statement**: The angle of contact (θ) is greater than 90 degrees, so the adhesive force is greater than the cohesive force.
- **Analysis**: This statement is also true. When the angle of contact is greater than 90 degrees, it indicates that the cohesive forces are stronger than the adhesive forces.

### Step 3: Analyze the Third Statement
- **Statement**: When the angle of contact is 90 degrees, the cohesive force is equal to the adhesive force.
- **Analysis**: This statement is true. At an angle of contact of 90 degrees, the forces balance out, meaning cohesive and adhesive forces are equal.

### Step 4: Analyze the Fourth Statement
- **Statement**: If the radius of the capillary is reduced to half, the rise in the liquid column becomes 4 times.
- **Analysis**: This statement is false. The height (h) of the liquid column in a capillary tube is inversely proportional to the radius (r) of the tube, as described by the formula:
\[ h \propto \frac{1}{r} \]
If the radius is reduced to half (r/2), the height will actually become:
\[ h' = 2h \]
Thus, the rise in the liquid column does not become 4 times but rather doubles.

### Conclusion
The fourth statement is false, and therefore, the answer is option D.

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