What is the formula for calculating the efficiency of a machine?

Efficiency is a measure of how well a machine converts input work into useful output work. The appropriate formula for calculating the efficiency of a machine is given by the relationship that compares the useful work output to the work input. This relationship is represented mathematically as follows:

Efficiency = (Output work ÷ Input work) × 100%

The multiplication by 100% converts the ratio into a percentage, making it easier to interpret the efficiency as a proportion of the total work input that is converted into useful work output. A higher percentage indicates a more efficient machine, meaning it effectively transforms a larger portion of the input work into output work.

In contrast to the formula for efficiency, other options provided are either incorrect calculations or do not reflect the concept of efficiency in terms of input versus output. For example, the formula involving input divided by output would yield a reciprocal that does not accurately define efficiency, and simply subtracting input work from output work does not relate to the concept of efficiency either. Additionally, the relationship of work done over time is a measure of power, not efficiency. Therefore, option A is the only choice that accurately describes how to calculate the efficiency of a machine.