To determine the correct expression that defines force using SI units, we need to understand the fundamental relationship given by Newton's Second Law of Motion. Newton's Second Law states that force (F) is the product of mass (m) and acceleration (a). Mathematically, this law is expressed as:
[tex]\[ F = m \cdot a \][/tex]
Next, let's consider the SI units involved in this relationship:
- Mass (m) is measured in kilograms (kg).
- Acceleration (a) is measured in meters per second squared (m/s²).
When we multiply mass by acceleration:
[tex]\[ \text{kilogram} \cdot \left( \frac{\text{meter}}{\text{second}^2} \right) = \text{N (Newton)} \][/tex]
So the unit of force in the International System of Units (SI) is the Newton (N), and it is defined as:
[tex]\[ 1 \, \text{Newton (N)} = 1 \, \text{kilogram (kg)} \cdot \frac{1 \, \text{meter (m)}}{(\text{second})^2} \][/tex]
In the given choices:
- A. [tex]\( 1 \, \text{N} = 1 \, \text{kg} \cdot \frac{m}{s} \)[/tex]
This option is incorrect because it lacks the squared term for seconds in the denominator.
- B. [tex]\( 1 \, \text{N} = 1 \, \text{kg} \cdot \frac{m}{s^2} \)[/tex]
This option is correct as it accurately reflects the units of force according to Newton’s Second Law.
- C. [tex]\( 1 \, \text{J} = 1 \, \text{kg} \cdot \frac{m}{s} \)[/tex]
This option is incorrect because it describes a joule (J), which is a unit of energy, not force.
- D. [tex]\( 1 \, \text{J} = 1 \, \text{kg} \cdot \frac{m}{s^2} \)[/tex]
This option is incorrect for the same reason as option C; it describes energy, not force.
Based on the above analysis, the correct expression that describes force using SI units is:
[tex]\[ \boxed{1 \, \text{N} = 1 \, \text{kg} \cdot \frac{m}{s^2}} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
