AIIMS 2006 Physics Fluid Mechanics Assertion Reason Question

Let's break down the question regarding the assertion and reason related to the floating of a thin stainless steel needle on water.

Assertion:

A thin stainless steel needle can lay floating on a still water surface.

Reason:

Any object floats when the buoyancy force balances the weight of the object.

Correct Answer: B

Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

Explanation:

1. Understanding the Assertion:

   • A thin stainless steel needle can indeed float on the surface of water due to the phenomenon of surface tension. Although steel is denser than water, the needle can float because a very thin needle does not exert enough force to break the surface tension of the water. This allows it to remain on the surface without sinking.

2. Understanding the Reason:

   • The reason given states that "any object floats when the buoyancy force balances the weight of the object." This statement is generally true according to Archimedes' principle. According to this principle, the buoyant force ($F_b$) acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object, which can be expressed mathematically as: $F_b = \rho_{fluid} \cdot V_{displaced} \cdot g$ where:
   • $\rho_{fluid}$ is the density of the fluid,
   • $V_{displaced}$ is the volume of the fluid displaced,
   • $g$ is the acceleration due to gravity.

   For an object to float, the buoyant force must equal the weight of the object ($W$): $F_b = W$ or $\rho_{fluid} \cdot V_{displaced} \cdot g = m \cdot g$ where $m$ is the mass of the object.

3. Why the Reason is Not the Correct Explanation for the Assertion:

   • While the reason accurately describes how objects float, it does not apply directly to the needle's situation. The needle floats not primarily due to its buoyancy balancing its weight (which it could do if it were a larger object that sinks), but rather due to surface tension. Surface tension creates an upward force that keeps the needle afloat even though its density is greater than that of water. Therefore, the reason does not explain the assertion correctly.

Clarifying Other Options:

• Option A: This option states that both the assertion and reason are true, and that the reason correctly explains the assertion. This is incorrect because, as discussed, while both statements are true, the reason does not explain the assertion specifically in the context of the needle.

• Option C: This option claims that the assertion is true but the reason is false. This is incorrect because the reason is indeed true; it just does not apply correctly to the assertion.

• Option D: This option states that both the assertion and reason are false. This is incorrect because both statements are true.

Summary:

In summary, the assertion that a thin stainless steel needle can float is true due to surface tension, and the reason provided is also true in a general context of floating objects. However, the reason does not specifically explain why the needle floats, making option B the correct choice.