Directions: For the Assertion (A) and Reason (R) given below, choose the correct alternative. Assertion (A): An iron ball floats on mercury but sinks in water. Reason (R): The specific gravity of iron is more than that of mercury.

Introduction / Context:
This assertion–reason question checks understanding of density (specific gravity) and floating or sinking of objects in different liquids. It uses the example of an iron ball in water and in mercury to see whether students know how relative densities decide floating behaviour and whether they can identify an incorrect statement about specific gravity.

Given Data / Assumptions:

• Assertion (A): An iron ball floats on mercury but sinks in water.
• Reason (R): The specific gravity of iron is more than that of mercury.
• We assume basic physics knowledge of density and Archimedes principle.
• We must assess the truth of A and R and whether R explains A.

Concept / Approach:
An object floats in a liquid if its density is less than the density of the liquid and sinks if its density is greater. Specific gravity is simply density compared to water density. Mercury is known to be a very dense liquid metal. Iron has density greater than water, but less than mercury. These facts are central for deciding whether the iron ball floats or sinks in each case and for assessing the correctness of the reason.

Step-by-Step Solution:
Step 1: Evaluate Assertion (A). Iron has density significantly greater than water, so an iron ball placed in water will sink. Mercury has density much greater than iron. Because mercury is more dense than iron, the iron ball placed on mercury will float. Therefore, the assertion that an iron ball floats on mercury but sinks in water is true.Step 2: Evaluate Reason (R). The statement says that the specific gravity (relative density) of iron is more than that of mercury. This is incorrect. Mercury is more dense than iron, so its specific gravity is greater than that of iron.Step 3: Since the reason directly contradicts correct scientific facts, R is false.Step 4: A is true and R is false, so R cannot be a correct explanation for A. In fact, the correct explanatory statement would be that the specific gravity of mercury is greater than the specific gravity of iron and that the specific gravity of iron is greater than that of water.

Verification / Alternative check:
We can recall typical density values taught in textbooks. Water density is about 1 gram per cubic centimetre, iron is about 7 to 8, and mercury is around 13.5. The object with density 7 to 8 will sink in density 1 but float on density 13.5. This simple comparison confirms that the relative density ordering is water less than iron less than mercury, not the other way around as implied by the reason.

Why Other Options Are Wrong:
Option a requires both A and R to be true and R to explain A, which fails because R is false. Option b also assumes R is true. Option d suggests Assertion (A) is false, which conflicts with the correct analysis of floating behaviour based on real density values.

Common Pitfalls:
Some students may confuse which substance is heavier per unit volume and may think of iron as heavier than mercury because they are more familiar with solid iron objects. Another common error is not distinguishing between absolute heaviness and density, forgetting that volume also matters. Always think in terms of density when analysing floating and sinking problems.

Final Answer:
The correct evaluation is that Assertion (A) is true but Reason (R) is false.