Which one of the following statements is incorrect?

Options

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

Answer

To determine which statement is incorrect, we will analyze each option one by one.

### Step-by-Step Solution:

1. **Statement A: Limiting value of static friction is directly proportional to the normal reaction.**
- The limiting value of static friction (Fs) can be expressed as:
\[ F_s = \mu_s \cdot N \]
where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal reaction force.
- From this equation, it is clear that \( F_s \) is directly proportional to \( N \). Therefore, Statement A is **correct**.

2. **Statement B: The friction force opposes the relative motion.**
- By definition, friction always acts in the direction opposite to the relative motion between two surfaces in contact. Thus, Statement B is also **correct**.

3. **Statement C: Rolling friction is smaller than sliding friction.**
- There are three types of friction: static friction, kinetic (or sliding) friction, and rolling friction. Generally, the order of the coefficients of friction is:
\[ \mu_s > \mu_k > \mu_r \]
This indicates that rolling friction (μr) is indeed smaller than sliding friction (μk). Therefore, Statement C is **correct**.

4. **Statement D: 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:
\[ \mu = \frac{F_s}{N} \]
Since both \( F_s \) (force) and \( N \) (normal force) have the same dimensions (force), the dimensions cancel out, making the coefficient of friction a dimensionless quantity. Therefore, Statement D is **incorrect**.

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

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