Work done by a force on an object is zero, if

Options

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

Answer

To determine when the work done by a force on an object is zero, we can analyze the formula for work done. The work done (W) by a force (F) is given by the equation:

\[ W = F \cdot S \]

where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( S \) is the displacement of the object in the direction of the force.

### Step-by-step Solution:

1. **Understanding the Formula**: The formula for work done shows that work is the product of the force applied and the displacement in the direction of that force.

2. **Setting Work Done to Zero**: According to the question, we need to find conditions under which the work done is zero. Therefore, we set the equation to zero:
\[ W = F \cdot S = 0 \]

3. **Analyzing the Equation**: For the product \( F \cdot S \) to equal zero, at least one of the factors must be zero. This gives us two possibilities:
- \( F = 0 \) (no force is applied)
- \( S = 0 \) (no displacement occurs)

4. **Conclusion**: Since the question specifies that there exists a force, we can conclude that the only viable condition for the work done to be zero is when the displacement \( S \) is zero. This means that if an object does not move from its initial position, the work done on it is zero.

### Final Answer:
The work done by a force on an object is zero if the displacement of the object is zero.

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