Work done by friction in case of pure rolling

Options

A. is always zero
B. is always positive
C. is always negative
D. may be positive,negative or zero

Explanation

### Step-by-Step Solution:

1. **Understanding Pure Rolling Motion**:
- In pure rolling motion, an object (like a ball or a wheel) rolls without slipping. This means that the point of contact between the rolling object and the surface is momentarily at rest relative to the surface.

2. **Identifying the Role of Friction**:
- In pure rolling, the friction involved is static friction. This type of friction prevents slipping between the rolling object and the surface.

3. **Analyzing the Work Done by Friction**:
- Work done (W) is calculated using the formula:
\[ W = F \cdot d \]
where \( F \) is the force and \( d \) is the displacement in the direction of the force.

4. **Considering the Displacement**:
- In pure rolling, the point of contact does not move relative to the surface. Therefore, the displacement \( d \) at the point of contact due to static friction is zero.

5. **Calculating Work Done**:
- Since the displacement \( d = 0 \), the work done by the static friction force can be calculated as:
\[ W = F_f \cdot 0 = 0 \]
- Here, \( F_f \) is the static friction force, which acts to prevent slipping.

6. **Conclusion**:
- Therefore, the work done by friction in the case of pure rolling is always zero.

### Final Answer:
The work done by friction in the case of pure rolling is **0**.

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