Question

Which of the following is a correct unit of energy? a) \(\mathrm{kg} \mathrm{m} / \mathrm{s}^{2}\) c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) e) \(\mathrm{kg}^{2} \mathrm{~m}^{2} / \mathrm{s}^{2}\) b) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}\) d) \(\mathrm{kg}^{2} \mathrm{~m} / \mathrm{s}^{2}\)

Short answer

Answer: The correct unit of energy is c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\).

Step-by-step solution

Define the Joule (J)

We know that the SI unit of energy is the Joule (J), named after the English physicist James Prescott Joule. It can be defined as the work done by a one Newton (N) force through a distance of one meter. In other words, 1 Joule = 1 N × 1 m. We also know that 1 N = \(\mathrm{kg} \mathrm{m} / \mathrm{s}^{2}\), which makes 1 J = \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\). Now, we are ready to compare each unit to this Joule unit.

Comparing the given choices

We will now compare each of the given options to the Joule's unit: a) \(\mathrm{kg} \mathrm{m} / \mathrm{s}^{2}\) - This is the unit for force (Newtons), not energy. c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) - This matches the unit for Joules (energy). e) \(\mathrm{kg}^{2} \mathrm{~m}^{2} / \mathrm{s}^{2}\) - This does not match the unit for Joules (energy). b) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}\) - This is the unit for angular momentum, not energy. d) \(\mathrm{kg}^{2} \mathrm{~m} / \mathrm{s}^{2}\) - This does not match the unit for Joules (energy).

Identify the correct unit

From the comparison of each given option, it is evident that option c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) matches the Joule's unit for energy. Therefore, the correct unit of energy is: c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\).