Question

Limiting friction is
A) Directly proportional to the area of contact
B) Inversely proportional to the area of contact
C) Independent on the area of contact
D) All of these

Answer 1

Hint: The limiting friction is maximum static friction ${F_s}$max or ${F_L}$.
According to Rule of friction: ${F_L} \propto N$
\[{F_L}\; = \;{\mu _L}N\]
${F_L} = $ limiting friction, \[{\mu _L} = \]coefficient of limiting friction
$N = $ Normal or reaction

Complete step by step answer:
Limiting friction: Friction between the surface and object depends on coefficient of friction and weight of object or the normal reaction force that is exerted in order to oppose the weight.

So, the expression of friction force applied to the object.
Normal (N) $ = $ mg
Adding to formula, ${F_L} = {\mu _L}N$
${\mu _L}N = $ Coefficient of limiting friction
${F_L} = {\mu _L}N$
${F_L} = {\mu _L}Mg$
Now come to the question, the surface of bodies is not smooth, it has irregular surface the frictional force between bodies is due to these irregularities interacting with each other. If one is to determine the actual surface area of two bodies that is in contact, it is much smaller than that of the apparent contact area when they are placed such that they are attached.
So, the deformation of the surface of bodies due to normal force makes the frictional force independent of shape and apparent area of contact and dependent only on the normal force.

So, the correct answer is “Option C”.

Note:
Analyze the factor dependent upon limiting friction and found that it is independent of smooth area.Also we have to remember some concept about the limiting force.