Question

Which one of the following statements is incorrect?
A. frictional force opposes the relative motion
B. rolling friction is smaller than sliding friction
C. coefficient of sliding friction has dimensions of length
D. limiting value of static friction is directly proportional to normal reaction

Answer 1

Hint: First, read and discuss friction between two bodies. The simplest case to understand the frictional force will be by applying a force on a body on a rough horizontal floor. Frictional force between two bodies is given as $f=\mu N$, where $\mu$ is the coefficient of friction and N is the normal force between the bodies.

Complete step-by-step answer:
Let us first discuss some points on friction.
Friction is the force that opposes the relative motion between two bodies. When you try to slide two bodies over one another, the frictional force comes into play. When the two bodies slide, there is a relative motion between the surfaces of the bodies and friction opposes this motion.
In other words, we can say that friction does not like the surfaces to move apart from each other. It wants the surfaces to be in contact.
Suppose a body is lying on a horizontal floor. Friction between the body and the floor is dependent on the normal force exerted by the body on the floor. Frictional force is directly proportional to the normal force (N).
Friction is also directly proportional to a quantity called coefficient of friction ($\mu$).$\mu$ depends on adhesion between the bodies and rough of the bodies. We all know about roughness and maybe that is the first thing that comes to our mind when we talk about friction.
Adhesion is the force of attraction between the molecules of the two surfaces.
Therefore, the friction is given as $f=\mu N$.
As we can see, f has dimension of force and N also has dimension of force. Therefore, $\mu$ has no dimensions.
Now, let us discuss types of friction.
For this, consider a body on a rough horizontal floor. Now, suppose we apply a force on the body to move it. We find that the body does not move for a certain range of force (case 1) and after a limit, the body starts to move (case 2).
In case 1, according to Newton’s law, when we apply an unbalanced force on the body the body must move. The force that we apply is balanced by the frictional force. Therefore, the body does not move. However, this friction has a limit. If the applied force is greater than the limit of the frictional force, the force on the body is unbalanced and it starts to move. This type of friction is called static friction (${{\mu }_{s}}$). The maximum of static friction is given as ${{f}_{\max }}={{\mu }_{s}}N$.
In case 2, when the applied force is greater than the maximum static friction, the body moves. When the body moves, the adhesion between the body and the surface is lessened.
Therefore, the coefficient of friction becomes less. This coefficient is called the coefficient of kinetic friction (${{\mu }_{k}}$).
If the body that we have considered has a circular surface, we say that the body is rolling. And the friction that is applied on the body is called rolling friction. The coefficient of friction is called the coefficient of rolling friction (${{\mu }_{r}}$). The value of ${{\mu }_{r}}$ is the least among the three coefficients of friction.
Now if we want the order of the values of coefficients of frictions, then it follows as:
${{\mu }_{s}}$>${{\mu }_{k}}$>${{\mu }_{r}}$.
With the discussed data above, we can compare the given options and find the incorrect option.
The options A, B and D matches with the data but option C is incorrect.

Option C says that coefficient of sliding friction has dimensions of length, whereas we know that coefficient of friction is dimensionless.
Hence, the correct answer for the question is option C.

Note: It may be important to note that static friction is a variable force whereas kinetic friction and rolling friction are constant forces for two given bodies. Static friction is equal to the force applied on the body, if the force applied is less than the maximum static friction.