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, we can break down the concepts involved 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 does not slide. This implies that the linear velocity of the center of mass (V_cm) and the angular velocity (ω) are related by the equation:
\[ V_{cm} = R \cdot \omega \]
where R is the radius of the sphere.

2. **Velocity of the Point of Contact**:
- At the point of contact with the ground, the velocity is momentarily zero. This is because, as the sphere rolls, the bottom-most point is instantaneously at rest relative to the ground.

3. **Acceleration of the Point of Contact**:
- Even though the velocity of the point of contact is zero, it can still have acceleration. As the sphere rolls, this point moves upwards and then downwards, indicating that it is accelerating vertically.

4. **Friction Force**:
- The friction force acting on the rolling sphere can be zero or non-zero depending on whether the sphere is accelerating or moving with constant velocity. If the sphere is rolling with constant velocity, the friction force can be zero. However, if it is accelerating, then static friction acts in the direction opposite to the acceleration.

5. **Work Done by Friction**:
- The work done by friction is zero when the point of contact does not move relative to the ground. Since the displacement of the point of contact in the direction of the friction force is zero, the work done is:
\[ W = F \cdot d \cdot \cos(\theta) = 0 \]
where \(d\) is the displacement at the point of contact, which is zero.

### Conclusion:
Based on the analysis, the correct statements regarding the spherical body rolling without slipping are:
- The velocity of the point of contact is zero.
- The acceleration of the point of contact is not zero.
- The friction force may or may not be zero depending on whether the sphere is accelerating.
- The work done by friction is zero.