Which of the following statements is correct?

Correct Answer: Work done can be positive or negative depending on the direction of force.

Step-by-Step Explanation:

Work done ($W$) by a force acting on an object is defined as the scalar product of the force vector ($F$) and the displacement vector ($s$). Mathematically, it is expressed as:

$W=F\cdot s\cdot \cos \left(\theta \right)$

where $\theta$ is the angle between the direction of the applied force and the direction of displacement.

The sign of the work done depends on the direction of the force relative to the motion (displacement):

1. Positive Work Done: When force and displacement are in the same direction ($0°\le \theta <90°$), $\cos \left(\theta \right)>0$, making the work done positive. For example, pushing a box forward.

2. Negative Work Done: When force acts in the direction opposite to displacement ($90°<\theta \le 180°$), $\cos \left(\theta \right)<0$, making the work done negative. For example, the force of friction opposing motion.

3. Zero Work Done: When force is perpendicular to displacement ($\theta =90°$), $\cos (90°)=0$, so work done is zero.

Therefore, work done depends on both force and displacement, and it can be positive or negative depending on the direction of the applied force relative to the displacement.