Correct Option
Assertion (A) states that an iron ball floats on mercury but gets immersed in water. This statement is true.
The principle of buoyancy dictates whether an object floats or sinks in a fluid. An object floats if its density (or specific gravity) is less than that of the fluid, and it sinks if its density is greater.
The specific gravity of iron is approximately 7.21.
The specific gravity of mercury is approximately 13.56.
The specific gravity of water is approximately 1.0.
Since the specific gravity of iron (7.21) is less than that of mercury (13.56), an iron ball floats on mercury.
Conversely, since the specific gravity of iron (7.21) is greater than that of water (1.0), an iron ball sinks in water.
Therefore, Assertion (A) is factually correct.
Reason (R) states that the specific gravity of iron is more than that of mercury. This statement is false.
As established, the specific gravity of iron (approximately 7.21) is significantly less than the specific gravity of mercury (approximately 13.56). Mercury is a much denser liquid than iron.
Therefore, Reason (R) is factually incorrect.
Given that Assertion (A) is true and Reason (R) is false, option 3 accurately reflects the relationship between the two statements.
Incorrect Options
Options 1, 2, and 4 are incorrect as they misrepresent the truthfulness of either the Assertion or the Reason, or both.
Options 1 and 2 are incorrect because Reason (R) is false, contradicting their premise that both A and R are true.
Option 4 is incorrect because Assertion (A) is true, not false, and Reason (R) is false, not true.