Which of the following is not a unit of energy? a) newton-meter b) joule c) kilowatt-hour d) \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) e) all of the above

Short Answer

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A) Newton-meter B) Joule C) Kilowatt-hour D) \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) E) All of the above Answer: E) All of the above

Step by step solution

01

Option A: Newton-meter

The Newton-meter (N.m) is also known as the joule (J), which is the SI unit of energy. A Newton is a unit of force and can be expressed as \(\operatorname{kg} \mathrm{m} / \mathrm{s}^{2}\). When we multiply force by the distance (meter), we get the unit of energy, which is \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\). Hence, the newton-meter is a unit of energy.
02

Option B: Joule

As mentioned in the previous option, the joule (J) is the SI unit of energy and is equal to \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\). Thus, the joule is a unit of energy.
03

Option C: Kilowatt-hour

The kilowatt-hour (kWh) is a unit of energy used in measuring electrical energy. It represents the amount of energy consumed by a device using 1 kilowatt (\(10^{3}\) watts) for 1 hour. A watt is a unit of power, which is equal to one joule per second. To convert kilowatt-hour into joules, we multiply by the number of seconds in an hour and the conversion factor from kilowatts to watts: \(1 \, \mathrm{kWh} = 1 \times 10^{3} \, \mathrm{W} \times 3600 \, \mathrm{s} = 3.6 \times 10^{6} \, \mathrm{J}\). Therefore, the kilowatt-hour is a unit of energy.
04

Option D: \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\)

The unit \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) is the same as the unit of the joule, which is the SI unit of energy. Hence, this option is also a unit of energy.
05

Conclusion

After analyzing each option, it is clear that all of the given units are units of energy. Therefore, the correct answer is option E: "all of the above" is not a unit of energy since it implies that not any of the options is a unit of energy, but in fact, all of them are.

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