Which one of the following statements is incorrect?

Options

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

Answer

To determine which statement is incorrect among the provided options, we will analyze each statement one by one.

### Step 1: Analyze the Statements
1. **Statement 1**: Rolling friction is smaller than sliding friction.
- This statement is **correct**. Generally, rolling friction is less than sliding friction due to the nature of how the surfaces interact when rolling compared to sliding.

2. **Statement 2**: The coefficient of sliding friction has dimensions of length.
- This statement is **incorrect**. The coefficient of friction is a dimensionless quantity. It is defined as the ratio of the frictional force to the normal force, both of which have dimensions of force (mass × acceleration) and thus cancel out, leaving a dimensionless ratio.

3. **Statement 3**: The frictional force opposes the relative motion.
- This statement is **correct**. By definition, friction always acts in the opposite direction to the motion of the object or the impending motion.

4. **Statement 4**: The limiting value of static friction is directly proportional to the normal reaction.
- This statement is **correct**. The limiting static friction can be expressed as \( F_s = \mu_s N \), where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force. This indicates a direct proportionality.

### Conclusion
After analyzing all the statements, we find that **Statement 2** is incorrect.

### Final Answer
The incorrect statement is: **The coefficient of sliding friction has dimensions of length.**

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