When a body is rolling without slipping on a rough horizontal surface, the work done by friction is :

Options

A. Always zero
B. May be zero
C. Always positive
D. Always negative

Answer

To solve the problem of determining the work done by friction when a body is rolling without slipping on a rough horizontal surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Rolling Without Slipping**:
- When a body rolls without slipping, there is a specific relationship between the linear velocity of the center of mass (v) and the angular velocity (ω) of the body. This relationship is given by the equation:
\[ v = r \cdot \omega \]
where \( r \) is the radius of the rolling body.

2. **Identifying the Role of Friction**:
- In rolling motion, friction is necessary to prevent slipping. It provides the torque needed for the body to rotate. However, it does not do work in this scenario.

3. **Analyzing the Point of Contact**:
- At the point of contact between the rolling body and the surface, there is no relative motion. This means that the point of contact does not move relative to the surface while the body rolls.

4. **Calculating Work Done by Friction**:
- The work done by a force is defined as:
\[ \text{Work} = \text{Force} \times \text{Displacement} \]
- Since the point of contact does not move (displacement is zero), the work done by the friction force can be expressed as:
\[ \text{Work} = f \times 0 = 0 \]
where \( f \) is the friction force.

5. **Conclusion**:
- Therefore, the work done by friction when a body is rolling without slipping on a rough horizontal surface is zero.

### Final Answer:
The work done by friction is **zero**.