A block A of mass 2 kg rests on another block B of mass 8 kg which rests on a horizontal floor. The coefficient of friction between A and B is 0.2, while that between B and floor is 0.5. When a horizontal force of 25 N is applied on the block B, the force of friction between A and B is

The correct answer is Zero.

Let us carefully analyze the forces acting on the system to understand why the friction between blocks A and B is zero.

Given Information:
Mass of block A, m_A = 2 kg
Mass of block B, m_B = 8 kg
Coefficient of friction between A and B, μ_AB = 0.2
Coefficient of friction between B and floor, μ_Bf = 0.5
Applied horizontal force on B, F = 25 N
Acceleration due to gravity, g = 10 m/s²

Step 1: Find the maximum static friction between Block B and the floor.

The normal force exerted by the floor on Block B equals the combined weight of both blocks (since A sits on B):

N_{\mathrm{floor}}=(m_A+m_B)\times g=(2+8)\times 10=100\text{N}

The maximum static friction force that the floor can exert on Block B is:

f_{\mathrm{max\; (floor)}}={\mu }_{\mathrm{Bf}}\times N_{\mathrm{floor}}=0.5\times 100=50\text{N}

Step 2: Determine whether Block B moves.

The applied force on Block B is 25 N, which is less than the maximum friction force from the floor (50 N). This means the floor's friction is more than enough to keep Block B stationary.

Therefore, Block B does not move.

Step 3: Analyze the motion of Block A and the friction between A and B.

No horizontal force is applied directly to Block A. The only horizontal force that could act on A is friction from the surface of Block B.

Since Block B itself is stationary (it does not slide under A), there is no relative motion between A and B, and more importantly, no tendency of relative motion between them either — because the external force is applied to B, not to A.

Block A has no reason to slide on Block B. The system is in complete static equilibrium. The friction force between two surfaces only arises when there is actual or impending relative motion between them.

Conclusion:

Since neither block moves, and since no net horizontal force acts on Block A to create any tendency of sliding between A and B, the friction force between A and B is:

f_{\mathrm{AB}}=0\text{N (Zero)}

The key insight here is that the applied 25 N force on Block B is insufficient to overcome the 50 N maximum friction between B and the floor. So the entire system remains at rest, and the friction between A and B is Zero.