If the work done is zero, then the angle between the force and displacement is

Options

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

Answer

To solve the problem, we need to understand the relationship between work done, force, displacement, and the angle between them.

### Step-by-Step Solution:

1. **Understand the Formula for Work Done**:
The formula for work done (W) is given by:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( W \) = work done
- \( F \) = magnitude of the force applied
- \( d \) = magnitude of the displacement
- \( \theta \) = angle between the force and displacement vectors

2. **Identify the Condition Given**:
We are told that the work done is zero:
\[ W = 0 \]

3. **Analyze the Formula**:
From the formula \( W = F \cdot d \cdot \cos(\theta) \), if \( W = 0 \), then either:
- The force \( F = 0 \) (which is not the case here as we are looking for an angle), or
- The displacement \( d = 0 \) (which again is not the case), or
- The term \( \cos(\theta) = 0 \)

4. **Determine the Angle**:
The cosine of an angle is zero at specific angles. The angle \( \theta \) for which \( \cos(\theta) = 0 \) is:
\[ \theta = 90^\circ + n \cdot 180^\circ \quad (n \in \mathbb{Z}) \]
The simplest case is when \( \theta = 90^\circ \).

5. **Conclusion**:
Therefore, if the work done is zero, the angle between the force and displacement must be \( 90^\circ \).

### Final Answer:
The angle between the force and displacement when the work done is zero is \( 90^\circ \).