Problem 56 - Master Resource Book in JEE Main Physics

Question

Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes \((a)\), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion When height of a tube is less than calculated height of liquid in the tube, the liquid does not overflow. Reason The meniscus of liquid at the top of the tube becomes flat.

Step-by-Step Solution

Answer

(b) Both statements are true, but the reason is not the explanation of the assertion.

Step 1: Understand the Assertion

The assertion states that if the calculated height of the liquid is greater than the height of the tube, the liquid will not overflow. This means that the tube is not tall enough to hold the entire calculated volume of liquid.

Step 2: Understand the Reason

The reason states that the meniscus of the liquid at the top becomes flat. This implies that when the tube fills completely, the curvature at the top of the liquid changes.

Step 3: Evaluate the Assertion and Reason

The assertion is true because when the calculated height of the liquid exceeds the tube height, under normal circumstances, one would expect an overflow. However, it mentions no overflow occurs. The reason provided can be true as the meniscus becoming flat can prevent the liquid from completely spilling over, but a flattening meniscus alone does not prevent overflow when the liquid exceeds tube capacity.

Step 4: Determine the Relationship

Even though both statements can be true individually, the reason does not explain why the liquid does not overflow. Overflow prevention relates more to surface tension effects not solely described by the meniscus flattening.

Key Concepts

Fluid Mechanics

Fluid mechanics is a vibrant branch of physics dedicated to studying the behavior of fluids, both at rest and in motion. It encompasses the principles governing liquids and gases and how they interact with various forces.
Understanding fluid mechanics is crucial for many practical applications, such as designing ships, airplanes, hydraulic systems, and even weather modeling.

• Flow and Pressure: Fluids can flow in different patterns, such as laminar or turbulent flow. Pressure in a fluid can change depending on the fluid's velocity and height, which often requires consideration of Bernoulli's principle.
• Buoyancy: This is the upward force experienced by a body submerged in a fluid. The principle of buoyancy is key in explaining why objects float or sink in water.
• Viscosity: This is the measure of a fluid's resistance to flow. Thick honey is more viscous than water. Viscosity influences how fluids spread and how they flow through pipes.

By mastering these fluid mechanics principles, one can better understand and predict how everyday fluids behave under various conditions.

Surface Tension

Surface tension is a property that makes the surface layer of a liquid behave like a stretched elastic membrane. It plays a critical role in phenomena such as the formation of droplets, how insects can walk on water, and the rise of liquids in a capillary tube.

• Causes of Surface Tension: It arises due to cohesion, the attractive force between molecules in a liquid. Molecules at the surface are pulled inward by the molecules beneath, creating a surface that resists external force.
• Effects on Liquid Behavior: Surface tension explains why water beads on a surface, preventing it from spreading out naturally. It affects how high liquids rise in a tube, but it isn't the sole factor in overflow conditions.

Surface tension's effect is distinct when comparing different liquids, as it determines how a liquid interacts at interfaces with solid surfaces or other liquids.

Meniscus

In fluid mechanics, the meniscus is the curve seen at the surface boundary of a liquid in a container. This curve can be either concave or convex, depending on the liquid and the material of the container.
Understanding the meniscus is essential in precise liquid measurement and interpreting the behaviors of liquids in narrow tubes, which is vital to capillary action.

• Causes of Meniscus Formation: The meniscus forms due to the interactions between liquid molecules and the container wall. If adhesion (attraction to the wall) is stronger than cohesion (attraction between liquid molecules), the meniscus curves upwards, as seen with water in a glass tube.
• Role in Capillary Action: The shape and properties of the meniscus significantly affect capillary rise. In narrow tubes, a strong adhesion force can cause the liquid to climb, driven by surface tension. This force, along with surface tension, explains why liquids can rise or stay at certain levels in tubes, contradicting expectations of overflow.

Thus, the meniscus is a key player in understanding liquid behavior in tubes and measuring systems, greatly influenced by surface tension and adhesion forces.