Considering a body of mass m, radius R rotating with angular speed `omega` about the centre of the mass and with a velocity v of centre of mass, the most appropriate definition of rolling motion will be

Options

A. v = R `omega`
B. the point of contact is stationary
C. the point of contact is stationary with respect to the surface
D. the body purely rotates about the point of contact

Answer

To solve the question regarding the definition of rolling motion for a body of mass \( m \), radius \( R \), rotating with angular speed \( \omega \) and having a linear velocity \( v \) of the center of mass, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Rolling Motion**:
- Rolling motion occurs when a body rotates about its axis while simultaneously translating along a surface. For pure rolling without slipping, the point of contact with the surface must have zero velocity relative to the surface.

2. **Identify Key Points**:
- Let’s denote:
- \( v \): Linear velocity of the center of mass.
- \( R \): Radius of the body.
- \( \omega \): Angular velocity of the body.
- Point \( P \): The point of contact between the body and the surface.

3. **Velocity at the Point of Contact**:
- The linear velocity of the center of mass is \( v \).
- The tangential velocity at the point of contact due to rotation is given by \( R \omega \).

4. **Condition for Pure Rolling**:
- For pure rolling, the point of contact must be stationary with respect to the surface. This means that the net velocity at point \( P \) must be zero:
\[ v - R \omega = 0 \]
- Rearranging this gives:
\[ v = R \omega \]

5. **Conclusion**:
- The most appropriate definition of rolling motion is that the point of contact is stationary with respect to the surface. This implies that the linear velocity \( v \) of the center of mass is equal to the tangential velocity \( R \omega \) at the point of contact.

### Final Answer:
The most appropriate definition of rolling motion is that **the point of contact is stationary with respect to the surface**.