In case of negative wark, the angle between the force and displacement is

Options

A. 0
B. `45^(@)`
C. `90^(@)`
D. `180^(@)`

Explanation

To determine the angle between the force and displacement when negative work is done, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Work Done**:
The work done (W) by a force is given by the formula:
\[ W = F \cdot d = |F| |d| \cos \theta \]
where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement vectors.

2. **Identifying Negative Work**:
For work to be negative, the value of \(W\) must be less than zero:
\[ W < 0 \]
This occurs when \(\cos \theta < 0\).

3. **Analyzing the Cosine Function**:
The cosine function is negative in the following ranges:
- \(90^\circ < \theta < 270^\circ\)

4. **Finding Relevant Angles**:
- At \(\theta = 90^\circ\), \(\cos 90^\circ = 0\) (work done is zero).
- At \(\theta = 180^\circ\), \(\cos 180^\circ = -1\) (work done is negative).
- At angles between \(90^\circ\) and \(180^\circ\), the cosine value is negative, indicating negative work.

5. **Conclusion**:
The angle at which negative work is done is specifically at \(180^\circ\) (where the force is applied in the opposite direction to the displacement) and also in the range of \(90^\circ < \theta < 270^\circ\).

### Final Answer:
The angle between the force and displacement when negative work is done can be \(180^\circ\) or in the range of \(90^\circ < \theta < 270^\circ\).

---