Which one of the following statements is incorrect ?

Options

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

Answer

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

### Step-by-Step Solution:

1. **Statement 1: Friction force opposes the relative motion.**
- This statement is true. Friction always acts in the direction opposite to the relative motion of two surfaces in contact. For example, if you push a block to the right, the friction force will act to the left, opposing the motion.

2. **Statement 2: Limiting value of static friction is directly proportional to normal reaction.**
- This statement is also true. The limiting static friction (f_s) can be expressed as:
\[ f_s \leq \mu_s N \]
where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force. This indicates that the maximum static friction is directly proportional to the normal force.

3. **Statement 3: Rolling friction is smaller than sliding friction.**
- This statement is correct. Rolling friction is generally less than sliding friction. When an object rolls over a surface, it experiences less resistance compared to when it slides. This is why rolling objects (like balls or wheels) are easier to move than sliding objects.

4. **Statement 4: Coefficient of sliding friction has dimensions of length.**
- This statement is incorrect. The coefficient of friction (both static and kinetic) is a dimensionless quantity. It is defined as the ratio of the force of friction to the normal force. Since both forces have the same dimensions (force), their ratio is dimensionless.

### Conclusion:
The incorrect statement is **Statement 4**: "Coefficient of sliding friction has dimensions of length."

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