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

To solve the question regarding the work done by friction in the case of pure rolling, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understanding Pure Rolling**:
- In pure rolling motion, an object (like a sphere) rolls without slipping on a surface. This means that the point of contact between the object and the surface has zero velocity relative to the surface.

2. **Identify the Forces**:
- When the sphere is rolling on a rough surface, the frictional force acts at the point of contact. This frictional force is necessary to prevent slipping and to allow the sphere to roll.

3. **Velocity of the Contact Point**:
- In pure rolling, the velocity of the contact point (the point of the sphere that is in contact with the surface) is zero. This means that while the sphere is moving forward, the point touching the ground does not slide.

4. **Displacement of the Contact Point**:
- Since the contact point does not move (its displacement is zero), we can analyze the work done by the frictional force. Work done is defined as the product of force and displacement in the direction of the force.

5. **Calculating Work Done by Friction**:
- The formula for work done is given by:
\[ \text{Work Done} = \text{Force} \times \text{Displacement} \]
- In the case of pure rolling, since the displacement of the contact point is zero, the work done by the frictional force is:
\[ \text{Work Done} = \text{Friction Force} \times 0 = 0 \]

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

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

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