Work Definition and Units

Work done is defined as the force applied to an object multiplied by the distance the object travels in the direction of the force. Mathematically, Work = Force $\times$ Distance.

Unit Analysis

Let's analyze the units provided:

• The standard SI unit for force is the Newton (N). 1 N = 1 $\text{kg} \cdot \text{m}/\text{sec}^2$.
• The standard SI unit for distance is the meter (m).
• Therefore, the unit of work is N $\cdot$ m.
• Substituting the unit of force, 1 N $\cdot$ m = (1 $\text{kg} \cdot \text{m}/\text{sec}^2$) $\cdot$ m = 1 $\text{kg} \cdot \text{m}^2/\text{sec}^2$.
• This unit (1 $\text{kg} \cdot \text{m}^2/\text{sec}^2$) is also known as the Joule (J), the standard unit of work and energy.

Evaluating Options

Based on the analysis:

• Option 1: $\text{Kgm}^2/\text{sec}^2$ - This is equivalent to kg $\cdot$ m$^2$/sec$^2$, which is a unit of work (Joule).
• Option 2: $\text{Kgm}/\text{sec}^2$ - This is equivalent to kg $\cdot$ m/sec$^2$, which is the unit of force (Newton), not work.
• Option 3: Newton meter - This is the product of force (Newton) and distance (meter), hence a unit of work.
• Option 4: Joule - This is the standard SI unit of work.

The question asks for the unit that is NOT a unit of work. Option 2 represents the unit of force.

Conclusion

The unit $\text{Kgm}/\text{sec}^2$ represents force, not work. Therefore, it is NOT a unit of work.