Limiting Friction and its Independence

Friction is a force that opposes the relative motion between two surfaces in contact. When an object is in contact with a surface and an external force is applied to it, the frictional force acts in the opposite direction to the applied force. The maximum value of this frictional force is known as limiting friction.

The limiting friction between two bodies in contact is independent of certain factors. Let's discuss each option given in the question and determine which one is correct.

a) Nature of the surface in contact:
The nature of the surface in contact does affect the frictional force between two bodies. Different materials have different levels of roughness and smoothness, which results in different frictional forces. For example, the friction between two rough surfaces will be greater than the friction between two smooth surfaces. Therefore, the limiting friction is not independent of the nature of the surface in contact.

b) The area of the surface in contact:
The area of the surface in contact does not affect the limiting friction between two bodies. Whether the contact area is large or small, the maximum value of the frictional force remains the same. This is because the limiting friction depends on the nature of the materials and the normal reaction between the surfaces, but not on the area of contact. Therefore, the correct answer is option 'B'.

c) Normal reaction between the surfaces:
The normal reaction between the surfaces does affect the limiting friction. The normal reaction is the force exerted by one surface on another perpendicular to the plane of contact. The greater the normal reaction, the greater the limiting friction. Therefore, the limiting friction is not independent of the normal reaction between the surfaces.

d) None of the above:
As discussed above, the correct answer is option 'B' - the limiting friction between two bodies in contact is independent of the area of the surface in contact. It is determined by the nature of the materials and the normal reaction between the surfaces.

In conclusion, the limiting friction between two bodies in contact is independent of the area of the surface in contact. This means that even if the area of contact changes, the maximum value of the frictional force remains the same as long as the nature of the materials and the normal reaction between the surfaces remain constant.