Which of the following statement (s) is / are correct for a spherical body rolling without slipping on a rough horizontal ground at rest?

Options

A. The acceleration of a point in contact with ground is zero
B. The speed of some of the point (s) is ( are ) zero.
C. Friction force may or may be zero
D. Work done by friction may or may not be zero

Answer

To analyze the statements regarding a spherical body rolling without slipping on a rough horizontal ground at rest, we will evaluate each statement step by step.

### Step-by-Step Solution:

1. **Understanding Rolling Without Slipping**:
- A spherical body rolling without slipping means that the point of contact with the ground is momentarily at rest. The relationship between translational velocity (V) and angular velocity (ω) is given by the equation:
\[ V = \omega r \]
- Here, r is the radius of the sphere.

2. **Evaluating Statement 1**: "The acceleration of the point in contact with the ground is zero."
- For a rolling object, the point of contact does not move relative to the ground, but it does have an acceleration due to the rotation of the sphere. The acceleration of the point in contact is not zero because it experiences centripetal acceleration and tangential acceleration due to rotation.
- **Conclusion**: This statement is **incorrect**.

3. **Evaluating Statement 2**: "The speed of the point in contact with the ground is zero."
- Since the point of contact is at rest relative to the ground during rolling without slipping, its speed is indeed zero.
- **Conclusion**: This statement is **correct**.

4. **Evaluating Statement 3**: "The friction force may or may not be zero."
- The friction force is necessary for rolling without slipping. If the sphere is rolling at a constant speed (no acceleration), the friction force can be zero. However, if there is any acceleration, friction will be present to maintain the rolling condition.
- **Conclusion**: This statement is **correct**.

5. **Evaluating Statement 4**: "The work done by the friction may or may not be zero."
- Since the point of contact is at rest during pure rolling, the work done by the friction force is zero because work is defined as force times displacement in the direction of the force. If there is no displacement at the point of contact, the work done is zero.
- **Conclusion**: This statement is **incorrect**.

### Final Evaluation:
- The correct statements are:
- Statement 2: "The speed of the point in contact with the ground is zero." (Correct)
- Statement 3: "The friction force may or may not be zero." (Correct)

### Summary of Correct Statements:
- Statements 2 and 3 are correct.