Two bodies having the same mass, 2 kg each have different surface areas 50 m² and 100 m² in contact with a horizontal plane. If the coefficient of friction is 0.2, the forces of friction that come into play when they are in motion will be in the ratio

The correct answer is 1 : 1.

This question tests a fundamental concept in classical mechanics — the nature of kinetic (sliding) friction. Let's build the solution from first principles.

The Law of Kinetic Friction

The force of kinetic friction acting on a body is given by:

f_k={\mu }_k\times N

where:

— {\mu }_k is the coefficient of kinetic friction
— N is the normal reaction force from the surface

Key Insight: Friction Does NOT Depend on Contact Area

Notice that the formula for friction force contains no term for surface area. This is one of the classic laws of friction (Amontons' Laws), which states that the force of friction is independent of the apparent area of contact.

This might seem counterintuitive, but here's the physical reasoning: when you increase the contact area, the same total weight is spread over a larger area, so the pressure per unit area decreases proportionally. The net frictional force remains the same.

Calculating Friction for Both Bodies

Given data:
— Mass of each body: m=2\text{kg}
— Surface areas: A_1=50\text{m²} and A_2=100\text{m²}
— Coefficient of friction: {\mu }_k=0.2
— g=10\text{m/s²}

Since both bodies lie on a horizontal plane and are in equilibrium vertically, the normal force equals the weight for each body:

N=mg=2\times 10=20\text{N}

This is the same for both bodies since they have the same mass.

Friction force on Body 1 (area = 50 m²):

f_1={\mu }_k\times N_1=0.2\times 20=4\text{N}

Friction force on Body 2 (area = 100 m²):

f_2={\mu }_k\times N_2=0.2\times 20=4\text{N}

Finding the Ratio

\frac{f_1}{f_2}=\frac{4}{4}=1:1

Conclusion: Even though the two bodies have different contact surface areas (50 m² and 100 m²), the frictional force on both is identical — 4 N each. The ratio of their friction forces is 1 : 1, because both bodies have the same mass, the same normal force, and experience the same coefficient of friction. The contact area is completely irrelevant to the magnitude of the friction force.