Efficiency as a dimensionless ratio

Steps:

• Efficiency is defined as useful output divided by total input, both in energy units like joules.
• Since numerator and denominator share the same units, they cancel, leaving no units.
• Common units like joule (energy), metre (length), and watt (power) measure physical quantities, not ratios.
• Thus, efficiency is expressed as a percentage or decimal without units.

Why A is correct:

• Efficiency is a dimensionless quantity per its formula (η = output/input), where units cancel.

Why the others are wrong:

• B: Joule measures energy, not a ratio like efficiency.
• C: Metre measures length, unrelated to efficiency.
• D: Watt measures power, not a unitless ratio.

Final answer: A