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The problem asks how a modification that doubles the power output of a motor, while keeping the energy input constant, would affect the efficiency.

### Efficiency Formula:
Efficiency (η) is given by the formula:

\[
\eta = \frac{\text{Power Output}}{\text{Energy Input}}
\]

- **Before the modification**, let's assume the power output is \(P\) and the energy input is \(E\). The efficiency is:

\[
\eta_{\text{initial}} = \frac{P}{E}
\]

- **After the modification**, the power output is doubled to \(2P\), but the energy input remains the same \(E\). The new efficiency is:

\[
\eta_{\text{new}} = \frac{2P}{E}
\]

### Conclusion:
The new efficiency is **twice the original efficiency** because the power output doubled while the energy input stayed the same. Therefore, the correct answer is:

- **It would double the efficiency of the motor.**

Would you like further explanation or have any other questions? Here are some related questions to explore:

1. What factors can limit the maximum efficiency of a motor?
2. How does the energy conversion process affect motor performance?
3. What happens if both power output and energy input increase proportionally?
4. How does the type of modification influence power efficiency?
5. Can motor efficiency ever exceed 100%? Why or why not?

**Tip:** Remember that efficiency is a ratio of output to input; any increase in output without a change in input will improve efficiency.

After a special modification, the power output of a motor is doubled, while the energy input remains the same. How would this affect the efficiency?

Understand how a motor's efficiency changes when its power output is doubled while maintaining the same energy input. This problem involves key mathematical concepts such as efficiency ratios and power analysis, suitable for Grades 8-12.

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