Which ratio below best defines the efficiency of simple machines ?

Options

A. `"useful work output "/"work input"xx100%`
B. `"work input "/"work output "xx100%`
C. `"theoretical mechanical advantage "/"actual mechanical advantage "xx100%`
D. `"useful work input "/"useful work output "xx100%`

Explanation

To determine the efficiency of simple machines, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Simple Machines**:
- Simple machines are devices that help us perform work by modifying the direction or magnitude of a force. Examples include levers, inclined planes, and wheels.

2. **Defining Efficiency**:
- Efficiency in the context of machines is a measure of how well a machine converts input energy into useful output work. It is typically expressed as a percentage.

3. **Formula for Efficiency**:
- The efficiency (η) of a simple machine can be defined using the following formula:
\[ \text{Efficiency} (\eta) = \left( \frac{\text{Useful Work Output}}{\text{Work Input}} \right) \times 100 \]
- Alternatively, it can also be expressed in terms of mechanical advantage:
\[ \text{Efficiency} (\eta) = \left( \frac{\text{Actual Mechanical Advantage}}{\text{Theoretical Mechanical Advantage}} \right) \times 100 \]

4. **Analyzing the Options**:
- The question asks which ratio best defines the efficiency of simple machines. The options provided typically include:
- A) Useful Work Output / Work Input
- B) Actual Mechanical Advantage / Theoretical Mechanical Advantage
- C) Theoretical Mechanical Advantage / Actual Mechanical Advantage
- From our definitions, we see that option A directly corresponds to the definition of efficiency.

5. **Conclusion**:
- Therefore, the ratio that best defines the efficiency of simple machines is:
\[ \text{Option A: Useful Work Output / Work Input} \]