Which one of the following statements is incorrect?

Options

A. Frictional force opposes the relative motion
B. Limiting value of static friction is direct,ly proportional to normal reaction
C. Rolling friction is smaller than sliding friction
D. Coefficeint of sliding friction has dimensions of length

Answer

To determine which statement is incorrect, let's analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1: Frictional force opposes the relative motion.**
- Friction is a force that acts to oppose the motion of an object. It acts in the opposite direction to that of the applied force or the direction of motion.
- **Conclusion:** This statement is **correct**.

2. **Statement 2: Limiting value of static friction is directly proportional to normal reaction.**
- The limiting value of static friction (F_s) can be expressed as \( F_s = \mu_s \cdot N \), where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force. This shows that static friction is proportional to the normal force.
- **Conclusion:** This statement is **correct**.

3. **Statement 3: Rolling friction is smaller than sliding friction.**
- It is a well-known fact that rolling friction (which occurs when an object rolls over a surface) is generally less than sliding friction (which occurs when an object slides over a surface).
- **Conclusion:** This statement is **correct**.

4. **Statement 4: Coefficient of sliding friction has dimensions of length.**
- The coefficient of friction (μ) is defined as the ratio of the force of friction to the normal force. Since both of these forces are measured in Newtons (N), the coefficient of friction is dimensionless (it has no units or dimensions).
- **Conclusion:** This statement is **incorrect**.

### Final Answer:
The incorrect statement is **Statement 4**.

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