Two blocks A and B of the same mass and surface finish are sliding on the same surface. Area of contact of A is twice that of the B. The frictional force between A and the surface is

Options

A. twice that of B
B. half that of B
C. same that of B
D. depends on the power supplied

Answer

To solve the problem, we need to analyze the frictional forces acting on blocks A and B. Here’s a step-by-step solution:

### Step 1: Understand the Given Information
- Both blocks A and B have the same mass (let's denote it as \( m \)).
- Both blocks are sliding on the same surface with the same surface finish, which implies they have the same coefficient of friction (\( \mu \)).
- The area of contact of block A is twice that of block B.

### Step 2: Calculate the Normal Force
The normal force (\( N \)) acting on each block can be calculated using the formula:
\[ N = m \cdot g \]
where \( g \) is the acceleration due to gravity.

Since both blocks have the same mass, the normal forces will be equal:
\[ N_A = N_B = m \cdot g \]

### Step 3: Write the Frictional Force Formula
The frictional force (\( F_f \)) can be calculated using the formula:
\[ F_f = \mu \cdot N \]
For block A:
\[ F_{fA} = \mu \cdot N_A \]
For block B:
\[ F_{fB} = \mu \cdot N_B \]

### Step 4: Substitute the Normal Forces
Since \( N_A = N_B = m \cdot g \), we can write:
\[ F_{fA} = \mu \cdot (m \cdot g) \]
\[ F_{fB} = \mu \cdot (m \cdot g) \]

### Step 5: Compare the Frictional Forces
Since both frictional forces depend on the same coefficient of friction and the same normal force, we can conclude:
\[ F_{fA} = F_{fB} \]

### Conclusion
The frictional force between block A and the surface is equal to the frictional force between block B and the surface. Thus, the frictional force between A and the surface is the same as that of B.