Answer :
To determine the correct combination of SI units for a force of 1 Newton (N), let's go through the process step-by-step.
1. Definition of Force:
According to Newton's Second Law of Motion, force (F) is defined as the product of mass (m) and acceleration (a):
[tex]\[ F = m \cdot a \][/tex]
2. SI Units for Mass:
The SI unit for mass is the kilogram (kg).
3. SI Units for Acceleration:
Acceleration is defined as the change in velocity per unit time. Its SI unit can be derived as follows:
- Velocity has the unit of meters per second (m/s).
- Acceleration, being the derivative of velocity, has the unit of meters per second squared (m/s²).
4. Combining Units for Force:
Substituting the units of mass and acceleration into the formula for force, we get:
[tex]\[ F = m \cdot a = (\text{kg}) \cdot \left(\frac{\text{m}}{\text{s}^2}\right) \][/tex]
Therefore, 1 Newton (N) is equal to 1 kilogram meter per second squared ([tex]\( \text{kg} \cdot \text{m/s}^2 \)[/tex]).
Now let's examine the given options:
- Option A: [tex]\( 1 \, \text{m/J.s} \)[/tex] — Meters per Joule second, which is not a correct combination for force.
- Option B: [tex]\( 1 \, \text{s}^2 \, \text{kg/m} \)[/tex] — Seconds squared kilogram per meter, which does not represent force.
- Option C: [tex]\( 1 \, \text{J/m-s}^2 \)[/tex] — Joules per meter second squared, not suitable for describing force.
- Option D: [tex]\( 1 \, \text{kg} \cdot \text{m/s}^2 \)[/tex] — Kilogram meter per second squared, which correctly represents the unit of force.
Based on this reasoning, the correct combination of SI units for 1 Newton (N) is:
[tex]\[ \boxed{1 \, \text{kg} \cdot \text{m/s}^2} \][/tex]
Thus, the correct answer is option D.
1. Definition of Force:
According to Newton's Second Law of Motion, force (F) is defined as the product of mass (m) and acceleration (a):
[tex]\[ F = m \cdot a \][/tex]
2. SI Units for Mass:
The SI unit for mass is the kilogram (kg).
3. SI Units for Acceleration:
Acceleration is defined as the change in velocity per unit time. Its SI unit can be derived as follows:
- Velocity has the unit of meters per second (m/s).
- Acceleration, being the derivative of velocity, has the unit of meters per second squared (m/s²).
4. Combining Units for Force:
Substituting the units of mass and acceleration into the formula for force, we get:
[tex]\[ F = m \cdot a = (\text{kg}) \cdot \left(\frac{\text{m}}{\text{s}^2}\right) \][/tex]
Therefore, 1 Newton (N) is equal to 1 kilogram meter per second squared ([tex]\( \text{kg} \cdot \text{m/s}^2 \)[/tex]).
Now let's examine the given options:
- Option A: [tex]\( 1 \, \text{m/J.s} \)[/tex] — Meters per Joule second, which is not a correct combination for force.
- Option B: [tex]\( 1 \, \text{s}^2 \, \text{kg/m} \)[/tex] — Seconds squared kilogram per meter, which does not represent force.
- Option C: [tex]\( 1 \, \text{J/m-s}^2 \)[/tex] — Joules per meter second squared, not suitable for describing force.
- Option D: [tex]\( 1 \, \text{kg} \cdot \text{m/s}^2 \)[/tex] — Kilogram meter per second squared, which correctly represents the unit of force.
Based on this reasoning, the correct combination of SI units for 1 Newton (N) is:
[tex]\[ \boxed{1 \, \text{kg} \cdot \text{m/s}^2} \][/tex]
Thus, the correct answer is option D.
