When a body travels a circular path such that its displacement is maximum equal to the diameter of the circle can we conclude work done is zero.

Options

A. Yes
B. No
C. data insufficient
D. none of these

Explanation

To solve the question, we need to analyze the situation described: a body moving along a circular path with a displacement equal to the diameter of the circle. We want to determine whether the work done is zero.

### Step-by-Step Solution:

1. **Understanding Displacement**:
- When a body travels along a circular path, its displacement is defined as the shortest distance between the initial and final points. In this case, if the body moves from point A to point B (which are at the ends of the diameter), the displacement is equal to the diameter of the circle.

2. **Identifying Work Done**:
- The work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \(F\) is the magnitude of the force,
- \(d\) is the displacement,
- \(\theta\) is the angle between the force and the displacement vector.

3. **Analyzing Forces**:
- In circular motion, the force acting on the body is typically the centripetal force, which acts towards the center of the circle. This force is always perpendicular to the displacement of the body when it moves along the circular path.

4. **Calculating Work Done**:
- If the force (centripetal force) is perpendicular to the displacement (which is the case here), then:
\[ \theta = 90^\circ \implies \cos(90^\circ) = 0 \]
Thus, the work done due to the centripetal force is:
\[ W = F \cdot d \cdot 0 = 0 \]

5. **Considering Other Forces**:
- However, if there are other forces acting on the body (like friction or any external force), the situation changes. The work done by these forces can be non-zero depending on their direction relative to the displacement.

6. **Conclusion**:
- Since we cannot definitively conclude that the only force acting is the centripetal force (which does no work), and we do not have information about other forces, we cannot determine the total work done. Therefore, the data provided is insufficient to conclude that the work done is zero.

### Final Answer:
The correct option is **"data insufficient"**.