Question

Why the force of friction on a body kept on the tabletop does not depend on the area of contact?

Answer 1

Although a larger area of contact between two surfaces would create a larger source of frictional forces, it also reduces the pressure between the two surfaces for a given force holding them together. Since pressure equals force divided by the area of contact, it works out that the increase in friction generating area is exactly offset by the reduction in pressure; the resulting frictional forces, then, are dependent only on the frictional coefficient of the materials and the force holding them together. If you were to increase the force as you increased the area to keep pressure the same, then increasing the area would increase the frictional force between the two surfaces.