Question

Which one of the following statements is incorrect ?

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

Answer 1

The Correct Option is D

The question asks us to identify the incorrect statement among the given options regarding friction. Let's analyze each statement to find the one that is incorrect:

1. Rolling friction is smaller than sliding friction.
   This statement is true. Rolling friction usually involves less contact area and deformation compared to sliding friction, which is why rolling friction is generally smaller.
2. Frictional force opposes the relative motion.
   This statement is true. By definition, friction is a force that opposes the relative motion or tendency of such motion between two surfaces in contact.
3. Limiting value of static friction is directly proportional to normal reaction.
   This statement is true. The limiting static friction, \(f_s\), is given by the equation: f_s = \mu_s N, where \(\mu_s\) is the coefficient of static friction, and \(N\) is the normal reaction force. This shows direct proportionality.
4. Coefficient of sliding friction has dimensions of length.
   This statement is incorrect. The coefficient of sliding friction, denoted by \(\mu_k\), is a dimensionless quantity. It does not have any physical dimensions such as length, mass, or time.

Based on the above analysis, the statement "Coefficient of sliding friction has dimensions of length" is incorrect. Hence, the correct answer is:

Coefficient of sliding friction has dimensions of length.