In case of negative work, the angle between the force and displacement isA 0°  B 45°  C 90° D 180°

Breakdown of the Problem

1. Understanding Negative Work: Work is defined as the product of force applied, displacement, and the cosine of the angle between the direction of the force and displacement.
2. Formula for Work: The formula is given by: $W = F \cdot d \cdot \cos(\theta)$ where $W$ is work, $F$ is force, $d$ is displacement, and $\theta$ is the angle between the force and the displacement.

Relevant Concepts

1. Negative Work Condition: Negative work occurs when the angle $\theta$ between the force and the displacement is such that $\cos(\theta)$ is negative.

Analysis and Detail

1. Angle Analysis:
   • For $0^\circ$: $\cos(0^\circ) = 1$ (Positive work)
   • For $45^\circ$: $\cos(45^\circ) = \frac{1}{\sqrt{2}} \approx 0.707$ (Positive work)
   • For $90^\circ$: $\cos(90^\circ) = 0$ (No work done)
   • For $180^\circ$: $\cos(180^\circ) = -1$ (Negative work)

Verify and Summarize

1. Conclusion: Since negative work occurs when the angle is $180^\circ$, the force is acting in the opposite direction to the displacement.

Final Answer

The angle between the force and displacement in the case of negative work is D: 180°.