A body is acted upon by a force. If work done by the force is zero, then which of the following is (are) possible?

Options

A. The body moves in such a way that point of application of the force remains fixed
B. The body remains stationary but the point of application of the force moves on the object
C. The force is always. Perpendicular to its acceleration
D. The velocity is always perpendicular to the force

Answer

To solve the question, "A body is acted upon by a force. If work done by the force is zero, then which of the following is (are) possible?", we will analyze the conditions under which the work done by a force can be zero.

### Step-by-Step Solution:

1. **Understanding Work Done**:
The work done \( W \) by a force \( F \) when it acts on an object that moves a displacement \( d \) is given by the formula:
\[ W = F \cdot d = F \cdot d \cos \theta \]
where \( \theta \) is the angle between the force and the direction of displacement.

2. **Condition for Zero Work**:
For the work done to be zero, either:
- The displacement \( d \) is zero (the object does not move).
- The angle \( \theta \) is \( 90^\circ \) (the force is perpendicular to the displacement).

3. **Analyzing Each Option**:
- **Option A**: "The body moves in such a way that the point of application of the force remains fixed."
- If the point of application of the force remains fixed, the body does not move in the direction of the force, which means the displacement is zero. Therefore, work done is zero. **This option is possible.**

- **Option B**: "The body always remains stationary but the point of application of the force moves on the object."
- If the body is stationary, the displacement is zero regardless of the force applied. Hence, work done is zero. **This option is also possible.**

- **Option C**: "The force is always perpendicular to its acceleration."
- If the force is perpendicular to the acceleration, it does not necessarily mean that the work done is zero. The acceleration could still result in displacement. Therefore, we cannot conclude that work done is zero. **This option is not possible.**

- **Option D**: "The force is always perpendicular to its velocity."
- If the force is perpendicular to the velocity, it means that the object is moving in a circular path (like centripetal force). In this case, the angle \( \theta \) is \( 90^\circ \), which results in zero work done. **This option is possible.**

4. **Conclusion**:
The options for which the work done by the force is zero are A, B, and D.

### Final Answer:
The possible options where the work done by the force is zero are: **A, B, and D**.