Understanding Force and its Units

Force is a fundamental concept in physics, described by Newton's second law of motion. The law states that the force acting on an object is directly proportional to its mass and acceleration.

The mathematical expression is:

$ F = m \times a $

Where:

• $F$ represents Force
• $m$ represents mass
• $a$ represents acceleration

Deriving the SI Unit of Force

To find the unit of force, we use the standard SI units for mass and acceleration:

• The SI unit of mass ($m$) is the kilogram ($kg$).
• The SI unit of acceleration ($a$) is meters per second squared ($m s^-2$).

Combining these units according to the formula $ F = ma $, the SI unit of force is:

$ \text{Unit of Force} = \text{Unit of mass} \times \text{Unit of acceleration} $

$ \text{Unit of Force} = kg \times m s^{-2} $

This unit, $kg m s^-2$, is also known as the Newton (N).

Analyzing the Options

Let's examine the given options based on the formula $ F = ma $:

• Option 1: $\text{gms}^{-1}$. This implies units of mass multiplied by time$^{-1}$ (e.g., $g \cdot s^{-1}$). This does not match the structure of force ($mass \times acceleration$).
• Option 2: $\text{gms}^{-2}$. This implies units of mass multiplied by time$^{-2}$ (e.g., $g \cdot s^{-2}$). This includes the mass and time components but lacks the necessary length component (like 'cm' for CGS units) for acceleration.
• Option 3: $\text{Kgms}^{-1}$. This implies units of mass multiplied by time$^{-1}$ (e.g., $kg \cdot s^{-1}$). This does not match the structure of force ($mass \times acceleration$).
• Option 4: $\text{Kgms}^{-2}$. This implies units of mass multiplied by time$^{-2}$ (e.g., $kg \cdot s^{-2}$). This option uses the SI unit for mass ($kg$) and the time component ($s^{-2}$) of acceleration. Although the length unit (like 'm') is missing, it represents the core components of the SI unit of force ($kg \cdot m s^{-2}$) among the choices provided.

Conclusion

Based on the analysis, Option 4 ($\text{Kgms}^{-2}$) is the most appropriate choice among the given options, representing the SI unit mass component multiplied by the time component of acceleration.