Force acting on a particle does some work only when
force has a component along the direction of motion of particle,
force has a component opposite to direction of motion of particle
force has a component perpendicular to direction of motion of particle.
IV. force is not able to move the particle. Which of the following statement(s)) is/are correct?

Options

A. I and II
B. II and III
C. III and IV
D. IV and I

Answer

To determine which statements about the work done by a force acting on a particle are correct, we need to analyze each statement based on the physics of work and force.

### Step-by-Step Solution:

1. **Understanding Work Done by a Force**:
The work \( W \) done by a force \( \mathbf{F} \) on an object that moves through a displacement \( \mathbf{s} \) is given by the formula:
\[ W = \mathbf{F} \cdot \mathbf{s} = F \cdot s \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force vector and the displacement vector.

2. **Analyzing Each Statement**:
- **Statement 1**: "Force has a component along the direction of motion of the particle."
- **Analysis**: If the force has a component in the direction of motion, it does positive work. This statement is **correct**.

- **Statement 2**: "Force has a component opposite to the direction of motion of the particle."
- **Analysis**: If the force acts opposite to the direction of motion, it does negative work. This statement is also **correct**.

- **Statement 3**: "Force has a component perpendicular to the direction of motion of the particle."
- **Analysis**: If the force is perpendicular to the motion, \( \cos(90^\circ) = 0 \), hence the work done is zero. This statement is **incorrect**.

- **Statement 4**: "Force is not able to move the particle."
- **Analysis**: If the force does not move the particle, then no work is done. This statement is **correct**.

3. **Conclusion**:
The correct statements regarding the work done by a force acting on a particle are:
- Statement 1: Correct
- Statement 2: Correct
- Statement 3: Incorrect
- Statement 4: Correct

### Final Answer:
The correct statements are 1, 2, and 4.