Which of the following statement (s) is /are correct ?

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 = 0^(@)` , if cohesive force = adhsive force .
D. If the radius of capillary is reduced to half , the rise of liquid column becomes 4 times .

Answer

To determine which of the statements regarding contact angle are correct, we need to analyze each statement based on the principles of fluid mechanics, particularly focusing on cohesive and adhesive forces.

### Step-by-Step Solution:

1. **Understanding Contact Angle**:
- The contact angle is defined as the angle formed at the interface where a liquid meets a solid surface. It is determined by drawing tangents to the liquid surface and the solid surface at the point of contact.

2. **Analyzing Statement 1**:
- "If the angle of contact is less than 90 degrees, then cohesive force is less than adhesive force."
- When the contact angle is less than 90 degrees, it indicates that the adhesive forces (between the liquid and solid) are stronger than the cohesive forces (between the liquid molecules). This statement is **correct**.

3. **Analyzing Statement 2**:
- "If the angle of contact is greater than 90 degrees, then cohesive force is greater than adhesive force."
- A contact angle greater than 90 degrees suggests that the cohesive forces are stronger than the adhesive forces, leading the liquid to bead up on the surface. This statement is **correct**.

4. **Analyzing Statement 3**:
- "Angle of contact is zero if cohesive force is equal to adhesive force."
- If cohesive and adhesive forces are equal, the liquid will not have a defined contact angle of zero. Instead, it will still form an angle less than 90 degrees. Therefore, this statement is **incorrect**.

5. **Analyzing Statement 4**:
- "If the radius of the capillary tube is reduced to half, the rise of the liquid column becomes 4 times."
- The height of the liquid column in a capillary tube is inversely proportional to the radius of the tube. If the radius is halved, the height increases by a factor of 2, not 4. Thus, this statement is **incorrect**.

### Conclusion:
- The correct statements are **1 and 2**. Statements 3 and 4 are incorrect.