A machine has an efficiency of 80%. If the input work is 200J, the output work is?

1. Analyze the question

We are given the efficiency of a machine and the input work. We need to calculate the actual work output produced by the machine.

2. Explain the concept

Efficiency ($\eta$) is defined as the ratio of the useful work output to the total work input, expressed as a percentage. The formula is:

To find the work output, we rearrange the formula:

3. Show the solution

• Given: • Efficiency ($\eta$) = 80% • Work Input = 200J

• Calculation: $$\text{Work Output} = \frac{80}{100} \times 200\text{J}$$ $$\text{Work Output} = 0.8 \times 200\text{J}$$ $$\text{Work Output} = 160\text{J}$$

4. Identify the answer

Comparing our result to the given options, 160J corresponds to option B.

5. Exam Tip

Always remember that for any real machine, the efficiency must be less than 100% because some energy is always lost to friction or heat. If your calculation results in an output work higher than the input work, you have likely multiplied instead of divided by the efficiency percentage!