Which of the following unit–physical quantity pairs is incorrect?

Introduction / Context:
In physics, many special units are used for measuring length, volume, and other quantities. Examples include parsec for astronomical distances, barrel for measuring volumes of liquids such as oil, and light year for very large distances in space. This question presents three unit–quantity pairs and asks you to identify which pairing is incorrect.

Given Data / Assumptions:

• Pair I: Parsec – Distance.
• Pair II: Barrel – Liquid (volume).
• Pair III: Light year – Time.
• We assume standard definitions used in astronomy and trade.

Concept / Approach:
A parsec is an astronomical unit of distance defined based on parallax measurements. A barrel is a unit of volume commonly used in the petroleum industry to measure liquid quantities. A light year, despite having the word year in its name, is defined as the distance light travels in one year in vacuum, not a unit of time. Therefore, the first two pairs correctly associate units with distance and volume, while the third pair incorrectly associates a distance unit with time. So only pair III is incorrect.

Step-by-Step Solution:
Step 1: Consider pair I: Parsec – Distance. A parsec is defined as the distance at which 1 astronomical unit subtends an angle of 1 arcsecond. This is clearly a measure of distance, so pair I is correct. Step 2: Consider pair II: Barrel – Liquid. A barrel is a traditional unit of volume used for liquids such as crude oil, typically equal to about 159 litres. Although the word liquid is used informally, the underlying quantity is volume, so the pairing is effectively correct. Step 3: Consider pair III: Light year – Time. A light year is defined as the distance that light travels in vacuum in one year. It is therefore a unit of distance, not time. This makes the pairing with time incorrect. Step 4: Since I and II are correct and III is incorrect, only pair III is wrong. Step 5: Among the options given, the statement that only III is incorrect matches this analysis.

Verification / Alternative check:
Astronomy sources state that 1 parsec is approximately 3.26 light years, emphasizing that both parsec and light year are distance units. Oil industry standards use barrels as a unit of volume for crude oil, again confirming that the second pair relates a volume unit to liquids. No serious scientific reference treats light year as a time unit; instead, time is measured in seconds, years, and other direct time units, while light year is always quoted as a very large length scale.

Why Other Options Are Wrong:
Only I and III: This would imply parsec is incorrectly matched with distance, which is false because parsec is indeed a distance unit. Only II: This would imply barrel does not relate to measuring liquids, which contradicts common usage in trade and industry. All are correct: This would incorrectly treat light year as a time unit, which is not accepted in physics.

Common Pitfalls:
Students often get misled by the word year in light year and assume it must measure time. However, the correct interpretation is distance covered by light in one year. A helpful way to remember this is to note that the speed of light is in units of distance per time, so multiplying by a time (one year) gives a distance, not another time. Always check whether the name of a unit reflects its actual definition or is just historical terminology.

Final Answer:
The incorrect unit–physical quantity pair is Only III, because a light year is a unit of distance, not time.