Question

The force of friction (F) is equal to _________
(given $\mu = $ coefficient of friction and $R = $ normal reaction)
A. $\mu R$
B. $\dfrac{{\mu R}}{2}$
C. $2\mu R$
D. $\dfrac{{\mu R}}{3}$

Answer 1

Hint: According to the modern view, the friction between two bodies is due to the interatomic force of attraction between the body and the surface of another body at the point of contact. This phenomenon is called cold welding. The maximum opposition offered by the interatomic forces is known as limiting friction (limiting friction is maximum static friction). Using the laws of limiting friction, we can find the relation between the force of friction and the normal reaction.

Complete step by step answer:
Friction is an opposing force that comes into play when a body moves or tends to move on the surface of another body.
Friction is of two types:
1. External friction: This friction acts between the surfaces of two different bodies in contact.
2. Internal friction: This friction acts between different layers of the same liquid or gas, it is also called viscous force.
When the body is on the verge of moving on the surface of another body, the opposing force is called limiting friction. Once the body overcomes the limiting friction, the interatomic bonding between the body and the surface at the point of contact breaks, and the surface becomes comparatively smoother.
Laws of limiting friction –
The force of limiting friction is directly proportional to the normal reaction between 2 bodies in contact.
The force of limiting friction acts in a direction opposite to that along which the body is on the verge of moving.
The force of limiting friction is independent of the area of contact between 2 bodies provided the normal reaction between them remains the same.
The force of limiting friction between 2 bodies depends on the nature of the materials of 2 bodies and the state of their roughness.
Now, according to the first law,
 $
  F \propto R \\
  \therefore F = \mu R \\
 $
 Where F is the force of friction, R is the normal reaction between the two bodies and $\mu $ is the coefficient of friction.

So, the correct answer is “Option A”.

Additional Information:
External friction is of further of 3 types –
Static friction: It is that opposing which comes into play when one body tends to move on the surface of another body but the actual motion has not yet started.
Limiting friction: When the body is on the verge of moving on the surface of another body, the opposing force is called limiting friction. Once the body overcomes the limiting friction, the interatomic bonding between the body and the surface at the point of contact breaks, and the surface becomes comparatively smoother.
Kinetic friction: It is that opposing force which comes into play when the body actually moves on the surface of another body. Rolling friction is a type of kinetic friction; it comes into play when one body actually rolls on the surface of another body.

Note:
Students should be aware of the laws of limiting friction and understand the concept of friction and its types. The coefficient of friction is defined as the ratio of friction to the normal reaction between two bodies in contact. It has no units.
The force of limiting friction acts in a direction opposite to that along which the body is on the verge of moving.