Assertion–Reason (Buoyancy & Densities):\nAssertion (A): An iron ball floats on mercury but sinks in water.\nReason (R): The specific gravity (density) of iron is greater than that of mercury.

Introduction / Context:
This physics item tests Archimedes’ principle and relative densities to predict floating/sinking behavior.

Given Data / Assumptions:

• Iron density ~7.8 g/cm^3.
• Water density ~1.0 g/cm^3 (at ~4 °C).
• Mercury density ~13.6 g/cm^3.

Concept / Approach:
A body floats if its average density is less than the fluid’s or if the buoyant force can balance weight before full submergence. Iron is denser than water, so it sinks in water. Mercury is much denser than iron; an iron ball displaces enough mercury to balance its weight before submerging fully, hence it floats.

Step-by-Step Solution:
1) A: True—empirically, iron sinks in water and floats on mercury.2) R: False—the statement says iron is denser than mercury; in fact, mercury is denser than iron. That is why iron floats on it.3) Therefore, “A true, R false.”

Verification / Alternative check:
Compute relative densities: 7.8 < 13.6 confirms float on mercury.

Why Other Options Are Wrong:
Any option that accepts R as true contradicts well-known densities.

Common Pitfalls:
Reversing which material has greater density.

Final Answer:
A is true but R is false.