Question

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: When height of a tube is less then liquid rise in the capillary tube the liquid does not overflow. Reason: Product of radius of meniscus and height of liquid incapilling tube always remains constant. (A) a (B) \(b\) (C) c (D) d

Short answer

(C) If assertion is true, but reason is false.

Step-by-step solution

Understand the Assertion

The assertion states that "when the height of a tube is less than the liquid rise in the capillary tube, the liquid does not overflow." Capillary action is the ability of a liquid to flow against gravity into a narrow space due to surface tension and adhesive forces. Here, we should consider whether the liquid overflows when the height of the tube is less than the rise of the liquid or not.

Understand the Reason

The reason given is: "The product of the radius of the meniscus and the height of the liquid in the capillary tube always remains constant." This statement is related to the geometrical aspect of the meniscus formed by the liquid in the tube and isn't directly linked to overflow of liquid from the tube.

Analyze the Relation between Assertion and Reason

Now let's first evaluate if the assertion is correct or not. If the height of the tube is less than the liquid rise in the capillary tube, it means that the liquid will fill the entire available height of the tube. However, due to surface tension and adhesive forces, the liquid does not necessarily overflow even when there's no more space for it to rise. Hence, the assertion is true. Now, let's evaluate if the reason is true or not. The statement "Product of the radius of the meniscus and height of the liquid in the capillary tube always remains constant" is not accurate. The reason is because several factors, such as the size of the tube, its material and surface properties, and the nature of the liquid, affect both the meniscus radius and the height of the liquid. So, the reason is false. We have now determined that the assertion is true, but the reason is false. Based on this analysis, the correct answer is:

Answer

(C) If assertion is true, but reason is false.

Key concepts

Assertion and Reason Questions

In JEE Physics problems, assertion and reason questions are a common format used to test a student's comprehension. These questions usually consist of a statement (assertion) and an accompanying explanation (reason), and students need to determine the interrelationship between them. The challenge lies in evaluating each statement's validity independently, and then deciding how they relate to each other.
The possible options generally include:

• Both statements are true, and the reason correctly explains the assertion.
• Both assertions are true, but the reason does not explain the assertion correctly.
• The assertion is true, while the reason is false.
• Both the assertion and reason are false.

Effective tackling of such questions requires a clear understanding of the physics principles underlying both the statement and reasoning. It is crucial for students to dissect each statement, ensuring they comprehend its standalone truth before deciding on their dependency. Practicing these helps in honing analytical skills and understanding complex scientific concepts.

Capillary Action

Capillary action is a fascinating phenomenon where liquid rises in a narrow tube, defying gravity due to surface tension and adhesive forces. It allows fluids to flow against gravitational pull through capillary tubes. This effect is observable in everyday life and is fundamental in fields such as botany and medical science.
The mechanism involves two primary forces:

• Adhesive forces: Attraction between the molecules of the liquid and the surface of the tube, which encourages the liquid to spread along the surface.
• Cohesive forces: Attraction among the liquid molecules themselves, which allows the liquid to hold together.

When adhesive forces between the liquid and tube are strong enough, the liquid climbs up the tube. The height to which the liquid rises is influenced by factors such as the tube's radius, the liquid's density, and the surface tension. Smaller tubes allow higher rises, making capillary action more pronounced. Understanding capillary action helps in grasping concepts related to fluid dynamics and is crucial for solving physics problems related to liquid behavior in confined spaces.

Surface Tension

Surface tension is a key concept to understand when analyzing how liquids behave, particularly in phenomena like capillary action. It arises because the molecules at the liquid's surface are pulled inwards due to unbalanced molecular forces, creating a sort of 'film' that makes the surface resistant to external force.
Some key points about surface tension include:

• It is quantified as the force acting along the surface of a liquid per unit length.
  
• Surfactants can decrease surface tension, allowing the liquid to spread more easily.
• Surface tension allows certain insects to "walk" on water and is responsible for the spherical shape of droplets.

The role of surface tension is significant in processes such as droplet formation, the ascent of liquids through capillaries, and the behavior of bubbles. For students dealing with physics problems, understanding how surface tension operates can unveil answers to interrelated phenomena like capillarity, making it easier to approach problems that include assertion and reason formats. Awareness of its implications is crucial for interpreting situations where liquid surface interactions play a pivotal role.