What is the formula for efficiency in a mechanical system?

The formula for efficiency in a mechanical system is determined by comparing the useful output of work to the total input of work put into the system. The correct answer, which states that efficiency is calculated by dividing work output by work input, captures this relationship accurately.

Efficiency is expressed as a ratio or a percentage, indicating how well a machine converts the input work into useful output. By using the formula "work output divided by work input," one can assess the performance of the mechanical system. If a machine uses a significant amount of input work to produce a smaller amount of output work, its efficiency will be low. Conversely, if it produces a higher amount of useful output while using less input work, it demonstrates higher efficiency.

The other options do not correctly represent the concept of efficiency in engineering terms. For instance, multiplying work output by work input does not provide a meaningful measure of efficiency. Similarly, dividing work input by work output yields a value that is the inverse of efficiency, and subtracting work input from output does not produce a ratio relevant to efficiency. Understanding this formula is essential for evaluating the performance and sustainability of different mechanical systems.