To determine which expression correctly describes energy using SI units, let's examine each option step by step.
Energy in the SI system is measured in Joules. A Joule (J) is defined as the amount of energy required to move a one-kilogram mass a distance of one meter by applying a force of one Newton. This can be expressed in terms of other SI base units.
1. Newton (N) is the SI unit of force.
2. By definition, [tex]\(1 \text{ Newton (N)} = 1 \text{ kg} \cdot \text{m}/\text{s}^2\)[/tex].
Since energy is defined as force applied over a distance, and [tex]\(1 \text{ Joule (J)} = 1 \text{ Newton} \times 1 \text{ meter}\)[/tex], substituting the definition of Newton gives:
[tex]\[1 \text{ Joule (J)} = 1 \text{ kg} \cdot \frac{\text{m}}{\text{s}^2} \cdot \text{m} = 1 \text{ kg} \cdot \frac{\text{m}^2}{\text{s}^2}\][/tex]
Now, let's check each option:
Option A: [tex]\(1 J = 1 kg \cdot m^2 / s\)[/tex]
- Here, there is one 's' missing in the denominator. It should have [tex]\(s^2\)[/tex] in the denominator to correctly represent energy. Thus, this option is incorrect.
Option B: [tex]\(1 J = 1 kg \cdot m^2 / s^2\)[/tex]
- This matches the derived unit for Joules exactly, as [tex]\( 1 J = 1 \text{ kg} \cdot \frac{\text{m}^2}{\text{s}^2} \)[/tex]. Therefore, this option is correct.
Option C: [tex]\(1 J = 1 kg \cdot m / s\)[/tex]
- This does not match because it is missing one 'm' in the numerator and [tex]\(s\)[/tex] in the denominator should be squared. Thus, this option is incorrect.
Option D: [tex]\(1 J = 1 kg \cdot m / s^2\)[/tex]
- Here, there is one 'm' missing in the numerator. It should have [tex]\(m^2\)[/tex] in the numerator. Thus, this option is incorrect as well.
After evaluating each option, it is evident that Option B is the correct expression that describes energy using SI units:
[tex]\[ \boxed{1 J = 1 kg \cdot \frac{m^2}{s^2}} \][/tex]
Therefore, the correct answer is [tex]\( \boxed{2} \)[/tex].
