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 floor `F` of `25 N` is applied on the block `B` the force of friction between `A` and `B` is

Options

A. `(a)3 N`
B. `(b)4 N`
C. `(c)2 N`
D. `(d)zero`

Explanation

To solve the problem, we need to determine the force of friction between block A and block B when a horizontal force of 25 N is applied to block B. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the masses and coefficients of friction
- 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 the floor (μ_BF) = 0.5

### Step 2: Calculate the normal force acting on block B
The normal force (N) acting on block B is the combined weight of both blocks A and B.
\[ N = (m_A + m_B) \cdot g \]
Where \( g \) is the acceleration due to gravity, approximately \( 10 \, \text{m/s}^2 \).

Substituting the values:
\[ N = (2 \, \text{kg} + 8 \, \text{kg}) \cdot 10 \, \text{m/s}^2 = 10 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 100 \, \text{N} \]

### Step 3: Calculate the maximum frictional force between B and the floor
The maximum frictional force (F_friction_BF) that can act between block B and the floor is given by:
\[ F_{\text{friction\_BF}} = \mu_{BF} \cdot N \]
Substituting the values:
\[ F_{\text{friction\_BF}} = 0.5 \cdot 100 \, \text{N} = 50 \, \text{N} \]

### Step 4: Determine the applied force and compare it with the frictional force
An external force of 25 N is applied to block B. The frictional force between block B and the floor can resist up to 50 N. Since the applied force (25 N) is less than the maximum frictional force (50 N), block B will not move.

### Step 5: Analyze the effect on block A
Since block B does not move, block A will also not move relative to block B. Therefore, the force of friction between block A and block B will be equal to the force required to keep block A stationary with respect to block B.

### Step 6: Calculate the force of friction between A and B
Since block A is at rest relative to block B, the force of friction between them must be equal to the force that would be required to keep block A from sliding off block B. However, since block B is not moving, the frictional force between A and B is effectively zero.

Thus, the force of friction between block A and block B is:
\[ F_{\text{friction\_AB}} = 0 \, \text{N} \]

### Final Answer
The force of friction between block A and block B is **0 N**.

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