Choose the correct statements

Options

A. Surface tension is a vector quantity.
B. The angle of contact for pure water is `90^@. `
C. The tube required for water barometer is longer than that required for mercury barometer.
D. Archimedes principle does not hold good for free fall.

Answer

To solve the question of identifying the correct statements regarding surface tension, angle of contact, barometers, and Archimedes' principle, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement 1: Surface tension is a vector quantity.**
- **Analysis:** Surface tension is defined as the force per unit length acting at the surface of a liquid. It is a measure of the cohesive forces acting at the surface. However, surface tension itself is a scalar quantity, as it does not have a direction associated with it. The forces due to surface tension can be vector quantities, but surface tension itself is not.
- **Conclusion:** This statement is **incorrect**.

2. **Statement 2: The angle of contact for pure water is 90 degrees.**
- **Analysis:** The angle of contact (or contact angle) is the angle formed between the tangent to the liquid surface and the solid surface at the point of contact. For pure water, the angle of contact is typically 0 degrees when in contact with clean glass, meaning that the water wets the glass completely. An angle of 90 degrees would imply that the liquid does not wet the surface at all, which is not the case for pure water on glass.
- **Conclusion:** This statement is **incorrect**.

3. **Statement 3: The tube required for a water barometer is longer than that required for a mercury barometer.**
- **Analysis:** A barometer measures atmospheric pressure using a column of liquid. The height of the liquid column is determined by the density of the liquid. The density of mercury is approximately 13.6 times that of water. Therefore, to balance the same atmospheric pressure, the height of the water column (H_w) must be 13.6 times greater than the height of the mercury column (H_m). This means that a water barometer would require a much longer tube than a mercury barometer to measure the same atmospheric pressure.
- **Conclusion:** This statement is **correct**.

4. **Statement 4: The Archimedes principle does not hold good for free fall.**
- **Analysis:** Archimedes' principle states that an object submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced. This principle assumes that the fluid is at rest. In a free-fall situation, both the object and the fluid are accelerating downward at the same rate due to gravity, which means that the buoyant force effectively becomes zero. Therefore, Archimedes' principle does not apply in a free-fall condition.
- **Conclusion:** This statement is **correct**.

### Final Summary of Statements:
- Statement 1: Incorrect
- Statement 2: Incorrect
- Statement 3: Correct
- Statement 4: Correct

### Correct Statements:
- Statement 3 and Statement 4 are correct.