A force F accelerates a block of mass m on horizontal surface. The coefficient of friction between the contact surface is . The acceleration of m will be -

Options

A. `(F-mumg)/M`
B. zero
C. may be (A) or (B)
D. None of these

Answer

To find the acceleration of a block of mass \( m \) being acted upon by a force \( F \) on a horizontal surface with a coefficient of friction \( \mu \), we can follow these steps:

### Step 1: Identify the forces acting on the block
The forces acting on the block are:
- The applied force \( F \) acting horizontally.
- The frictional force \( f \) acting in the opposite direction to the applied force.

### Step 2: Determine the frictional force
The frictional force \( f \) can be calculated using the formula:
\[ f = \mu N \]
where \( N \) is the normal force. On a horizontal surface, the normal force \( N \) is equal to the weight of the block, which is given by:
\[ N = mg \]
Thus, the frictional force becomes:
\[ f = \mu mg \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force acting on the block is equal to the mass of the block multiplied by its acceleration \( a \):
\[ F - f = ma \]
Substituting the expression for the frictional force, we have:
\[ F - \mu mg = ma \]

### Step 4: Solve for acceleration \( a \)
Rearranging the equation to solve for acceleration \( a \):
\[ a = \frac{F - \mu mg}{m} \]

### Final Expression
Thus, the acceleration \( a \) of the block is given by:
\[ a = \frac{F}{m} - \mu g \]